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We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged mappings to expansive set-valued mappings that characterizes a type of strong calmness of the fixed point mapping. The second component to this analysis is an extension of the well-established notion of metric subregularity--or inverse calmness--of the mapping at fixed points. Convergence of expansive fixed point iterations is proved using these two properties, and quantitative estimates are a natural by-product of the framework. To demonstrate the application of the theory, we prove, for the first time, a number of results showing local linear convergence of nonconvex cyclic projections for inconsistent (and consistent) feasibility problems, local linear convergence of the forward-backward algorithm for structured optimization without convexity, strong or otherwise, and local linear convergence of the Douglas-Rachford algorithm for structured nonconvex minimization. This theory includes earlier approaches for known results, convex and non-convex, as special cases. Open Access Statement: This work is licensed under a Creative Commons Attribution 4.0 International License. You are free to copy, distribute, transmit, and adapt this work, but you must attribute this work as 'Mathematics of Operations Research. Copyright [c] 2018 The Author(s). https://doi.org/10.1287/moor.2017.0898, used under a Creative Commons Attribution License: https://creativecommons.org/hcenses/by/4.0/.' Funding: DRL was supported in part by the German-Israeli Foundation [Grant G-1253-304.6] and Deutsche Forschungsgemeinschaft Collaborative Research Center SFB755. NHT was supported by the German-Israeli Foundation [Grant G-1253-304.6], MKT was supported by Deutsche Forschungsgemeinschaft Research Training [Grant 2088] and the Alexander von Humboldt Foundation. Keywords: analysis of algorithms * feasibility * fixed points * Kurdyka-Lojasiewicz inequality * linear convergence * metric regularity * nonconvex * nonsmooth * proximal algorithms * subtransversality * transversality, 1. Introduction We present a program of analysis that enables one to quantify the rate of convergence of sequences generated by fixed point iterations of expansive set-valued mappings. The framework [...]

This paper is concerned with the question of reconstructing a vector in a finite-dimensional complex Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We present new invertibility results as well as an iterative algorithm that finds the least-square solution, which is robust in the presence of noise. We analyze its numerical performance by comparing it to the Cramer-Rao lower bound., Author(s): Radu Balan[sup.1] Author Affiliations: (1) Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, 20742, College Park, MD, USA Introduction This paper [...]

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same [...]

The local model fitting (LMF) method is one of the useful single-shot surface profiling algorithms. The measurement principle of the LMF method relies on the assumption that the target surface is locally flat. Based on this assumption, the height of the surface at each pixel is estimated from pixel values in its vicinity. Therefore, we can estimate flat areas of the target surface precisely, whereas the measurement accuracy could be degraded in areas where the assumption is violated, because of a curved surface or sharp steps. In this paper, we propose to overcome this problem by weighting the contribution of the pixels according to the degree of satisfaction of the locally flat assumption. However, since we have no information on the surface profile beforehand, we iteratively estimate it and use this estimation result to determine the weights. This algorithm is named the iteratively-reweighted LMF (IRLMF) method. Experimental results show that the proposed algorithm works excellently. OCIS codes: 240.0240, 240.6700.

This paper presents a new numerical procedure for the determination of the viscoelastic compliance properties of a matrix phase from a simple three-point bending test on a composite beam. The composite is modeled as elastic inclusions randomly dispersed throughout a viscoelastic matrix. It is also assumed that the spatial distribution of the inclusions in the composite is known or can be determined. Zevin's method of iterative functions is proposed for the determination of the matrix properties. Following a detailed explanation of the proposed scheme, a numerical verification is performed using three-dimensional finite-element (FE) analysis simulations. The proposed scheme was applied to the experimentally obtained creep compliance of the asphalt concrete beam. The obtained viscoelastic properties of the asphalt binder matrix phase were used as input into the FE model to simulate the behavior of the composite beam. An excellent comparison between the experimental data and the predicted beam deflections was observed. This shows that the proposed method is robust and it can be implemented to solve identification problems for viscoelastic composite materials. DOI: 10.1061/(ASCE)EM. 1943-7889.0000126 CE Database subject headings: Elasticity; Viscoelasticity; Numerical analysis; Asphalts; Mixtures; Composite materials; Pavements. Author keywords: Elasticity; Viscoelasticity; Numerical analysis; Asphalts; Mixtures; Composite materials; Pavements.

The non-autonomous Bloch equations modelling a driven 2-level atom in the presence of an off-resonant broadband squeezed vacuum (SV) field is treated analytically. This concerns iterative solutions valid for large SV detuning parameter but for arbitrary strength of the laser field. Computational results are presented for the averaged atomic variables for various data and compared with the resonant SV field case. The iterated analytical results for nonzero SV detuning are compared with the (exact) numerical solutions of the Bloch equations, hence we have an insight about the range of other system parameters (other than the Rabi frequency) for which the iterated solutions are valid to O([10.sup.-2]) or less. The main purpose of deriving these analytical results is to calculate analytically the transient fluorescent spectrum. For an initially ground-state atom, both the SV phase and detuning parameters induce pronounced asymmetrical spectrum in the strong field case. PACS Nos: 32.50.+d, 42.50.-p, 42.50.ct Nous etudions analytiquement les equations de Bloch qui modeelisent un atome a deux niveaux soumis a un champ laser en presence d'un champ du vide (SV) comprimee a large bande et hors resonance. Ceci touche les solutions iteratives pour de grands parametres de desyntonisation du SV, mais pour une intensite arbitraire du champ laser. Les resultats calcules sont presentes pour des variables atomiques moyennes pour diffeerentes donneees et compares avec le cas du champ SV resonant. Nous comparons les resultats analytiques iteeratifs pour un SV non nul avec les solutions numeriques (exactes) des equations de Bloch, ce qui nous donne un apenju du domaine des parametres du systeme autres que la frequence de Rabi, pour lequel les solutions iteratives sont valides a une precision de 0([10.sup.-2]) ou mieux. Le but principal de ces resultats analytiques est de calculer analytiquement le spectre de fluorescence transitoire. Pour un atome initialement dans le fondamental, la phase SV et les parametres de desyntonisation peuvent tous deux conduire a un spectre fortement asymetrique en champ fort. [Traduit par la Redaction], 1. Introduction From the early days of quantum optics, theoretical studies of the interaction of radiation fields with the simplest atomic structure, namely a two-level atom, has provided valuable information [...]

Making use of an iterated homogenization procedure in finite elasticity, an exact and explicit result is derived for the macroscopic response of Neo-Hookean solids reinforced by a random and isotropic distribution of rigid particles. The key theoretical and practical features of the result are discussed in light of comparisons with recent approximations and full-field simulations. [DOI: 10.1115/1.3197444]

An alternative approach to research is described that has been developed through a succession of significant construction management research projects. The approach follows the principles of iterative grounded theory, whereby researchers iterate between alternative theoretical frameworks and emergent empirical data. Of particular importance is an orientation toward mixing methods, thereby overcoming the existing tendency to dichotomize quantitative and qualitative approaches. The approach is positioned against the existing contested literature on grounded theory, and the possibility of engaging with empirical data in a 'theory free' manner is discounted. Emphasis instead is given to the way in which researchers must be theoretically sensitive as a result of being steeped in relevant literatures. Knowledge of existing literatures therefore shapes the initial research design; but emergent empirical findings cause fresh theoretical perspectives to be mobilized. The advocated approach is further aligned with notions of knowledge coproduction and the underlying principles of contextualist research. It is this unique combination of ideas which characterizes the paper's contribution to the research methodology literature within the field of construction management. Examples are provided and consideration is given to the extent to which the emergent findings are generalizable beyond the specific context from which they are derived. CE Database subject headings: Research; Theories; Methodology; Construction management. Author keywords: Contextualist research; Coproduction; Ground theory; Interpretive research; Research methodology. DOI: 10.1061/(ASCE)CO.1943-7862.0000027

We present the algorithm, error bounds, and numerical results for extra-precise iterative refinement applied to overdetermined linear least squares (LLS) problems. We apply our linear system refinement algorithm to Bjorck's augmented linear system formulation of an LLS problem. Our algorithm reduces the forward normwise and componentwise errors to O([[epsilon].sub.w]), where [[epsilon].sub.w] is the working precision, unless the system is too ill conditioned. In contrast to linear systems, we provide two separate error bounds for the solution x and the residual r. The refinement algorithm requires only limited use of extra precision and adds only O(mn) work to the O([mn.sup.2]) cost of QR factorization for problems of size m-by-n. The extra precision calculation is facilitated by the new extended-precision BLAS standard in a portable way, and the refinement algorithm will be included in a future release of LAPACK and can be extended to the other types of least squares problems. Categories and Subject Descriptors: G.1.3 [Numerical Analysis]: Numerical Linear Algebra--Linear systems (direct and iterative methods); error analysis General Terms: Algorithms, Reliability Additional Key Words and Phrases: Linear algebra, LAPACK, BLAS, floating-point arithmetic DOI = 10.1145/1462173.1462177.

We show that the convergence of modified Mann iteration, modified Mann iteration with errors, modified Ishikawa iteration, modified Ishikawa iteration with errors, modified Noor iteration, modified Noor iteration with errors, modified Smarandacheian multistep iteration and Smarandacheian multistep iteration with errors are equivalent for uniformly Lipschitzian strongly successively pseudocontractive maps in an arbitrary real Banach space. The results generalise and extend the results of several authors, including Rhoades and Soltuz [20, 21] and Rafiq [19]. Keywords modified Mann-Ishikawa iterations (with errors), modified Noor-multistep iteration (with errors), uniformly Lipschitzian maps, strongly successively pseudocontractive maps., [section]1. Introduction Let X be a real Banach space, and K a non-empty subset of X, T a self mapping of K and F(T), D(T) and I are the set [...]

This article investigates a nonlinear dispersive Zakharov-Kuznetsov ZK (3, 3, 3) equation. This equation governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) are implemented for solving the ZK equation. Homotopy results were compared with results of Adomian decomposition Method (ADM). The results reveal that the HPM and VIM are very effective, convenient and quite accurate to systems of nonlinear partial differential equations. Keywords: Zakharov-Kuznetsov equation, Variational, Homotopy perturbation method, INTRODUCTION The investigation of the traveling wave solution plays an important role in nonlinear science. These solutions may well describe various phenomena in nature, such as vibrations, solitons and propagation [...]

The main objective of the current work was to solve the multispecies predator-prey model.The techniques used here were called the variational iteration method (VIM) and the Adomian decomposition method (ADM). The advantage of this work is twofold. Firstly, the VIM reduces thecomputational work. Secondly, in comparison with existing techniques, the VIM is an improvementwith regard to its accuracy and rapid convergence. The VIM has the advantage of being more concise for analytical and numerical purposes. Comparisons with the exact solution and the fourth-orderRunge-Kutta method (RK4) show that the VIM is a powerful method for the solution of nonlinearequations. Key words: Variational iteration method (VIM), Adomian decomposition method (ADM), fourthorder Runge-Kutta method (RK4), multispecies predator-prey model, INTRODUCTION The variational iteration method (VIM) wasproposed by He (1) initially with the aims to solvefrontier physical problem. It has been applied to a wide class of deterministic and stochastic [...]

A novel low-complexity and provably convergent algorithm is proposed to find the sum capacity for vector Gaussian broadcast channels. Unlike the recently proposed sum-power constraint iterative waterfilling (SPC-IWF) algorithms, it has lower complexity and requires no additional precautions to ensure the convergence. We have proved analytically the convergence with probability one, and the computer simulations show that the proposed algorithm converges faster than the earlier variants of SPC-IWF algorithms. We formulate the problem in the context of a multiple-input multiple-output orthogonal frequency-division multiplexing system and discuss the simplifications provided by the block-diagonal channel structure. Index Terms--Broadcast channels, iterative waterfilling (IWF), multiple-input multiple-output (MIMO) systems, orthogonal frequency-division multiplexing (OFDM).

We present the design and testing of an algorithm for iterative refinement of the solution of linear equations where the residual is computed with extra precision. This algorithm was originally proposed in 1948 and analyzed in the 1960s as a means to compute very accurate solutions to all but the most ill-conditioned linear systems. However, two obstacles have until now prevented its adoption in standard subroutine libraries like LAPACK: (1) There was no standard way to access the higher precision arithmetic needed to compute residuals, and (2) it was unclear how to compute a reliable error bound for the computed solution. The completion of the new BLAS Technical Forum Standard has essentially removed the first obstacle. To overcome the second obstacle, we show how the application of iterative refinement can be used to compute an error bound in any norm at small cost and use this to compute both an error bound in the usual infinity norm, and a componentwise relative error bound. We report extensive test results on over 6.2 million matrices of dimensions 5, 10, 100, and 1000. As long as a normwise (componentwise) condition number computed by the algorithm is less than 1/max{10,[square root of (n)][[epsilon].sub.w], the computed normwise (componentwise) error bound is at most 2 max{10,[square root of (n)] * [[epsilon].sub.w]}, and indeed bounds the true error. Here, n is the matrix dimension and [[epsilon].sub.w] = [2.sup.-24] is the working precision. Residuals were computed in double precision (53 bits of precision). In other words, the algorithm always computed a tiny error at negligible extra cost for most linear systems. For worse conditioned problems (which we can detect using condition estimation), we obtained small correct error bounds in over 90% of cases. Categories and Subject Descriptors: G.1.3 [Numerical Analysis]: Numerical Linear Algebra--Linear systems (direct and iterative methods), Error analysis General Terms: Algorithms, Reliability Additional Key Words and Phrases: Linear algebra, LAPACK, BLAS, floating-point arithmetic

Performances of iterative blind deconvolution methods for motion-blurred images are usually reduced depending on the accuracy of the required initial guess of the blur. We examine this dependency, and a two-stage restoration procedure is proposed: First we perform a direct technique with a single straightforward process to produce a rough initial estimate of the blur, and then an iterative technique is employed to refine the blur estimate. Two common iterative techniques (the expectation-maximization and the Richardson-Lucy methods) are examined here and implemented in the combined direct-iterative modification for a variety of motion blur types. Results show that the combined method significantly improves the reliability of the deconvolution process.

A blind maximum likelihood equalization method is proposed for frequency selective fast fading Ricean channels. This method employs the expectation-maximization Viterbi algorithm (EMVA) developed in [1] for blind channel estimation and signal detection. Since the Viterbi algorithm (VA) is used to execute the E-phase of an expectation-maximization (EM) iteration, it requires that the observed sequence can be modelled as a finite-state hidden Markov process. We develop a hidden Markov model for frequency selective fast fading Ricean channels, so that the observed process can be viewed as the noisy output of a finite state machine (FSM), to which the VA is applicable. The EMVA is then employed to obtain a blind maximum likelihood estimate of the specular part of the channel and, for one special case, of a noise parameter measuring the total power of the additive and multiplicative channel noise components. Simulation results are presented which show that the EMVA achieves an accurate estimate of the channel specular part and has an error rate performance close to that of the maximum likelihood detector based on true parameters for the given FSM model. Index Terms--Blind equalization, expectation-maximization (EM) algorithm, Rayleigh fading channel, Ricean fading channel, Viterbi algorithm (VA).

An efficient accuracy-improvement scheme is proposed to analyze electromagnetic problems with conductive medium. This scheme is based on interpreting the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method as a special iterative solver for the Crank-Nicholson scheme. By applying an additional number of iterations to locations with relatively large field variation, the overall accuracy can be improved with little computational overhead. Special treatment of Iossy medium in the ADI-FDTD method is also addressed. Finally, numerical examples demonstrate the effectiveness of the proposed method. Index Terms--Alternating-direction implicit finite-difference time-domain (ADI-FDTD) method, conductive medium, iterative method, splitting error.

Byline: D. Neuenschwander (1) Author Affiliation: (1) Institut des Sciences Actuarielles, Universite de Lausanne, CH-1015, Lausanne, Switzerland Article History: Registration Date: 09/10/2004

Noncoherent communications via the Raleigh flat-fading channel with multiple transmit and receive antennas is examined. It is shown that, under specified conditions, turbo codes concatenated with differential space-time modulation codes can achieve a bit error rate(BER) that is lower than 10[superscript -4].

Iterative space-time multiuser detection schemes for multipath code division multiple access (CDMA) channels with multiple receive antennas are discussed. It is shown that exploiting diversities via space-time processing and multiuser detection provides improvement, compared with alternative processing methods.

Nonlinear optimal control problems usually require solutions using iterative procedures and, hence, they fall naturally in the realm of 2-D systems where the two dimensions are response time horizon and iteration index, respectively. The paper uses this observation to employ 2-D systems theory, in the form of unit memory repetitive process techniques, to investigate optimality, local stability, and global convergence behavior of an algorithm, based on integrated-system optimization and parameter estimation, for solving continuous nonlinear dynamic optimal control problems. It is shown that 2-D systems theory can be usefully applied to analyze the properties of iterative procedures for solving these problems. Index Terms--2-D systems, convergence, optimal control, stability, unit memory repetitive processes.

Iterative learning control (ILC) applies to control systems that perform the same finite-time tracking command repeatedly. It iteratively adjusts the command from one repetition to the next in order to reduce the tracking error. This creates a two-dimensional (2-D) system, with time step and repetition number as independent variables. The simplest form of ILC uses only one gain times one error in the previous repetition, and can be shown to converge to the zero-tracking error independent of the system dynamics. Hence, it appears very effective from a mathematical perspective. However, in practice, there are unacceptable learning transients. A zero-phase low-pass filter is introduced here to eliminate the bad transients. The main purpose of this paper is to supply a journal presentation of experiments on a commercial robot that demonstrate the effectiveness of this approach, improving the tracking accuracy of the robot performing a high speed maneuver by a factor of 100 in six repetitions. Experiments using a two-gain ILC reaches this error level in only three iterations. It is suggested that these two simple ILC laws are the equivalent for learning control, of proportional and PD control in classical control system design. Thus, what was an impractical approach, becomes practical, easy to apply, and effective. Index Terms--2-D systems, iterative learning control, precision motion control, robotics, zero-phase filtering.

This paper evaluates two-dimensional turbo product codes based on single-parity check codes (TPC/SPC) and low-density parity check (LDPC) codes for use in digital magnetic recording systems. It is first shown that the combination of a TPC/SPC code and a precoded partial response (PR) channel results in a good distance spectrum due to the interleaving gain. Then, density evolution is used to compute the thresholds for TPC/SPC codes and LDPC codes over PR channels. Analysis shows that TPC/SPC codes have a performance close to that of LDPC codes for large codeword lengths. Simulation results for practical block lengths show that TPC/SPC codes perform as well as LDPC codes in terms of bit error rate, but possess better burst error statistics which is important in the presence of an outer Reed-Solomon code. Further, the encoding complexity of TPC/SPC codes is only linear in the codeword length and the generator matrix does not have to be stored explicitly. Based on the results in the paper and these advantages, TPC/SPC codes seem like a viable alternative to LDPC codes. Index Terms--Data storage system, density evolution, iterative decoding, low-density parity check codes, message-passing decoding, partial response channels, precoding, turbo product codes.

Current radar applications require the design of high-power, differential phase shift ferrite circulators with increased bandwidth and better thermal performance. To meet these requirements, a magnetostatic/microwave/thermal method is proposed to model high-power ferrite devices. Magnetic losses are included in the model, which also has a temperature-dependent saturation magnetization and thermal conductivity. An iterative approach has been implemented which uses the power dissipated by the magnetic losses as the heat source for a thermal finite-element solver. Bias field, frequency, magnetic losses, and magnetization are used to determine the temperature profile in the ferrite for a given input power. The recommended operating region for temperature stability in high-power differential phase shift devices is deduced to be below subsidiary resonance and above low field loss. Index Terms--Ferrite-loaded waveguides, finite-element methods, iterative method, nonreciprocal wave propagation, temperature.

Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these […]

An iterative method of reconstructing degraded images is developed from consideration of a mixed-noise imaging situation. Both photon noise in the image itself and postdetection Gaussian noise are combined by use of the standard maximum-likelihood method to produce a mixed-expectation reconstruction technique that demonstrates good performance in the presence of both noise sources. The new algorithm is evaluated through computer simulations.

This paper presents a dual-loop iteration algorithm for steady-state determination of current-programmed direct current to direct current (dc-dc) switching converters. The methodology starts with separating the gate signal from the feedback circuit to the power stage in order to convert a closed-loop configuration into an open-loop one. The first iteration loop applies the Newton's method together with a time-domain simulation technique to find the steady-state state variables when the transformed configuration is operating at a constant duty cycle. The second iteration loop is to find the steady-state duty cycle using the secant method. The algorithm includes all of the advantages of a previously developed time-domain simulation technique and solves the nonconvergence problem in the single-loop iteration method, due to the amplifying effect of poor guess values of the state variables on the duty cycle in the feedback path during the iteration. A current-programmed boost converter is illustrated. The performances of the single-loop and the proposed methods are compared. The theoretical results are verified with the experimental measurements. Index Terms - Circuit simulation, dc-dc power conversion, iterative methods, Jacobian matrices, power electronics, switched mode power supplies, switching circuits.

An iterative technique is developed for frequency-domain plane wave scattering from electrically large composite bodies. An electric field integral equation (EFIE) formulation is employed in which the submatrices of the moment-method matrix are uncoupled and the current on each geometrically separable region of the composite body is solved independently using a direct method. The currents on the various subcomponents of the body are then recalculated within an outer iterative loop. The technique is applied to the case of a multiwavelength body of revolution (BOR) with two flat-plate attachments. This composite body iterative technique is shown to preserve the simplicity and attractiveness of an isolated BOR while maintaining current continuity across the structure without the use of additional junction currents. This new formulation also allows simple suppression of interior resonance effects normally associated with large closed conducting bodies. Index Terms - Electromagneric scattering, iterative methods, large bodies. method of moments.

This paper presents the application of nonempirical effective medium theories to describe composite mixtures of spherical inclusions within a host continuum. It is shown that the most common effective medium theories collapse into Bruggeman's asymmetric formula when they are implemented in an iterative scheme to extend their validity to higher volume fractions. Comparisons of dc and 4-GHz data show that of all the formulas Bruggeman's asymmetric formula corresponds best with experiment for large differences between the complex permittivities of the host and inclusion materials. Permeability values are also formulated and compared with experiment and a simple scheme is considered to extend the effective medium theories herein to a description of the diamagnetic effect of induced current in metal spherical inclusions. Index Terms - Effective medium, spherical inclusions, synthetic medium.

Research was conducted to investigate the computational complexity of the modified Newton-Raphson iteration (BMNR) and its convergence rate. Broyden's method of rank-1 updates were used to derive an algorithm that involved less computation and converged superlinearly. On the other hand, the MNR approach involved O(n4) iterations that converge quadratically. Also, the BMNR method maintains the favorable property that is completely general in its applicability.

Single-projection iterative reconstruction allows the use of high overrelaxation parameters. The parameters can be optimized in a pragmatic way by studying their influence on figures of merit extracted from the image. The resulting parameters are high in the beginning and drop down during further iteration. The value of the overrelaxation parameter which gives the best image after one iteration step is easily found. However, this value will change if an optimum image is postulated after two or more iteration steps. A procedure has been developed which rapidly finds the parameters to be used during a sequence of iteration steps to obtain optimum results for a later approximation. Comparing optimization during one and two steps, the initial parameters obtained with two-step optimization are about twice as high as those with one-step optimization, accelerating convergence by nearly a factor of two. Optimization within three or more steps again leads to different parameter sequences which, however, provide only minor convergence improvement. This indicates that different sequences of parameters may result in similar images, and parameters derived from a typical data set may be widely used for other data. Computation of new parameter sequences by the optimizing procedure is recommended if data from new equipment or with new characteristics have to be processed. Index Terms - Image reconstruction, positron emission tomography.

A proposed general iterative mapping system, which is derived from an information theoretic criterion of optimality, is presented. The generalized mapping function (GMF) encompasses a broad range of iterative algorithms which include maximum likelihood and least squares, and has the ability to unify their interpretation and analysis. Conditions for GMF convergence and a particular form of GMF mapping are described.

Dendrimers are a new class of macromolecules with unique structures and properties. They are constructed from ABn monomers and were synthesized in an iterative fashion. The use of dendrimers in molecular recognition and self-assembling systems, two important aspects of supramolecular chemistry were investigated. It was observed that the novel architecture of dendrimers can serve as a versatile platform for host-guests interactions.

Scheduling techniques for task and loop parallelism was examined to test its mapping iterative task computation on message-passing architectures. The directed acyclic graph scheduling is important in the performance of ITG scheduling. Results showed that algorithms performs well and is useful in mapping application in graphical parallel programming tools and run-time systems for irregular problems.

Correlation by means of phase windows that artificially create phase shifts is combined with the least-squares fit to provide a processing algorithm. A Young's pattern is correlated by means of the phase windows to generate four patterns with phase shifts of 0 [degree], 90 [degrees], 180 [degrees], and 270 [degrees]. The phase of the Young's pattern is derived from the four patterns. Then the derived phase is least-squares fitted to a phase plane. The above steps are repeated once to improve accuracy. Speckle noise is suppressed by the correlation operations, as well as a loop including phase calculation, fringe reconstruction, and smoothing. The magnitude and direction of the displacement associated with Young's pattern are determined from the phase plane. The algorithm takes less calculation time than the fast Fourier transform method and does so with improved accuracy. Software has been developed and is used in the experiment. Key words: Young's pattern, phase shift, iteration, least-squares fit.