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The accuracy of the adaptive cross approximation (ACA) algorithm, a popular method for the compression of low-rank matrix blocks in method of moment computations, is sometimes seriously compromised by unpredictable errors in the convergence criterion. This article proposes an alternative criterion based on global sampling of the error in the elements of the ACA compressed matrix. The sampling error depends not only on the size of the sample but also on the population distribution of the error, which makes it difficult to control the error independently of the underlying problem. However, as argued and demonstrated in this article, the distribution of the error converges to the same unique probability distribution function for all low-rank matrices. Complementing the sampling criterion with a simple mechanism to detect this convergence, we arrive at a criterion that controls the error irrespective of the underlying problem. As a practical example, the RCS of a moderate size metallic ogive is computed to illustrate the merits of the proposed criterion. The proposed algorithm may also be useful in other methods that approximate low-rank matrices by interpolation of a reduced set of its elements. [ABSTRACT FROM AUTHOR]

In high-speed analog-to-digital converters (ADCs), two main factors contribute to high power consumption. The first is the super linear relationship with the sampling rate; i.e., by doubling the sampling rate, the power consumption more than doubles. The second factor arises from the consumption of analog circuitry responsible to mitigate the jitter noise. By employing a multichannel sampling system, one can achieve high sampling rates by incorporating multiple low sampling-rate channels, which results in a linear scaling of power consumption with the number of channels. The main drawback of this system is the timing mismatch between the sampling channels. In this paper, we intend to jointly compensate the jitter noise and the timing mismatch between the channels using statistical methods. We first approximate the acquisition system and derive a stochastic model. Then, we propose an iterative maximum likelihood algorithm to estimate the parameters of the input signal. We further evaluate the Cramér-Rao lower bound (CRLB) for the estimation error to examine the proposed algorithm. Simulation results indicate that our algorithm is capable of closely following the CRLB curve for reasonable values of jitter noise and a wide range of timing mismatch errors. Moreover, it is shown that the mismatch-compensated multichannel sampling system performs almost equivalently to a single-channel high rate sampler without having its shortcomings. [ABSTRACT FROM AUTHOR]

To localize the wireless sensor networks nodes, only the hop-based information (i.e., hops’ number, average hop size, and so on) has been, so far, exploited by range-free techniques, with poor-accuracy, however. In this paper, we show that localization accuracy may greatly benefit from joint exploitation, at no cost, of the information already provided by the forwarding nodes (i.e., relays) between each anchor (i.e., position aware) and sensor nodes pair. As such, we develop a novel range-free localization algorithm, derive its average location estimation error (LEE) in closed-form, and compare it in LEE performance with the best representative algorithms in the literature. We show that the proposed algorithm outperforms them in accuracy. In contrast to the latter, we further prove that it is able to achieve an LEE average and variance of about 0 when the number of sensors is large enough, thereby achieving an unprecedented accuracy performance among range-free techniques. [ABSTRACT FROM PUBLISHER]

In this paper, an extremal eigenvalue problem corresponding to an inhomogeneous membrane which is composed of two different materials with different densities is investigated. The convergence of the finite element discretization and the error order for the smallest eigenvalue are obtained. A monotonic decreasing algorithm is presented to solve the discretized problem and numerical examples are given to demonstrate the error estimation as well as the efficiency of the method. [ABSTRACT FROM AUTHOR]