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Abstract: In this paper, we apply a complete pivoting strategy to compute the left-looking version of AINV preconditioner for linear systems. As the preprocessing, the MultiLevel Nested Dissection reordering has also been applied. We have used this preconditioner as the right preconditioner for several linear systems where the coefficient matrices have been downloaded from the University of Florida Sparse Matrix Collection. Numerical experiments presented in this paper indicate the effectiveness of such a complete pivoting on the quality of left-looking version of AINV preconditioner. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the bounds of the Perron root of a nonnegative irreducible matrix . Two new methods utilizing the relationship between the Perron root of a nonnegative irreducible matrix and its generalized Perron complements are presented. The former method is efficient because it gives the bounds for only by calculating the row sums of the generalized Perron complement or even the row sums of submatrices and . And the latter gives the closest bounds (just in this paper) of . The results obtained by these methods largely improve the classical bounds. Numerical examples are given to illustrate the procedure and compare it with others, which shows that these methods are effective. [Copyright &y& Elsevier]

Abstract: This paper discusses the spectral properties of the nonsymmetric saddle point matrices of the form with A symmetric positive definite, B full rank, and C symmetric positive semidefinite. A new sufficient condition is obtained so that is diagonalizable with all its eigenvalues real and positive. This condition is weaker than that stated in the recent paper [J. Liesen, A note on the eigenvalues of saddle point matrices, Technical Report 10-2006, Institute of Mathematics, TU Berlin, 2006]. [Copyright &y& Elsevier]

Abstract: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided. [ABSTRACT FROM AUTHOR]

Abstract: It is pointed out by Jiang and Wang (2005) , that the conversion formula from Bernstein into DP bases is incorrect for all even degrees and the conversion formula from DP into Bernstein bases is incorrect for every degree. Thus, in this paper we give some notes, corrections and new proofs for the relationship between these two NTP bases. [Copyright &y& Elsevier]

Abstract: In this paper, an inversion algorithm for a banded matrix is presented. The twisted decompositions of a banded matrix are given first; then the inverse of the matrix is obtained, one column at time. The method is about two times faster than the standard method based on the decomposition, as is shown with the analysis of computing complexity and the numerical experiments. [Copyright &y& Elsevier]

Abstract: The availability of explicit solutions, i.e. analytical relationships between the structural response and the design variables, allows a more direct and plain treatment of several structural problems. This paper is devoted to derive approximate explicit solutions in the framework of linear static analysis of finite element modeled structures with a given layout (fixed node positions). The proposed procedure is based on a factorization of the element stiffness matrix following the unimodal components concept, which allows a non-conventional assembly of the global stiffness matrix. The exact inversion of that matrix is a trivial task for the case of statically determinate structures, structures with few redundancies or few design variables. An approximate inverse of the stiffness matrix is herein derived for more general structural problems by resorting to the Sherman–Morrison–Woodbury formula. [Copyright &y& Elsevier]

Abstract: We propose a “fast” algorithm for the construction of a data-sparse inverse of a generalToeplitz matrix. The computational cost for inverting an N × N Toeplitz matrix equals the cost of four length-N FFTs plus an O(N)-term. This cost should be compared to the O(N log2 N) cost of previously published methods. Moreover, while those earlier methods are based on algebraic considerations, the procedure of this paper is analysis-based; as a result, its stability does not depend on the symmetry and positive-definiteness of the matrix being inverted. The performance of the scheme is illustrated with numerical examples. [Copyright &y& Elsevier]

Abstract: A central problem in the Jacobi-Davidson method is to expand a projection subspace by solving a certain correction equation. It has been commonly accepted that the correction equation always has a solution. However, it is proved in this paper that this is not true. Conditions are given to decide when it has a unique solution or many solutions or no solution. A refined Jacobi-Davidson method is proposed to overcome the possible nonconvergence of Ritz vectors by computing certain refined approximation eigenvectors from the subspace. A corresponding correction equation is derived for the refined method. Numerical experiments are conducted and efficiency of the refined method is confirmed. [Copyright &y& Elsevier]

We determine the conditions for uniqueness of the solutions of several completion problems including the positive semi-definite completion, the distance matrix completion, and the contractive matrix completion. The conditions depend on the existence of a positive semi-definite matrix satisfying certain linear constraints. Numerically, such conditions can be checked by existing computer software such as semi-definite programming routines. Some numerical examples are given to illustrate the results, and show that some results in a recent paper of Alfakih are incorrect. Discrepancies in the proof of Alfakih are explained. [Copyright &y& Elsevier]