This paper proposes improvements in the row and column samplings of the multilevel QR factorization method known as IES3, a fast integral equation solver previously proposed for efficient three-dimensional (3-D) param...
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This paper proposes improvements in the row and column samplings of the multilevel QR factorization method known as IES3, a fast integral equation solver previously proposed for efficient three-dimensional (3-D) parameter extraction. First, a rigorous Gram-Schmidt row sampling is developed to replace the row sampling algorithm in IES3, leading to a more stable algorithm. Second, to further enhance the efficiency of column sampling, a new scheme based on the idea of locating the interpolation points is presented. Error analyses indicate that the proposed schemes have higher accuracies than the original sampling in IES3, especially when the number of sampled points is small. The IES3 that uses one of these improved algorithms is called improved multilevel matrix QR factorization (IMLMQRF). These IMLMQRFs are applied in the magnetoquasistatic analysis of printed circuits on multilayered lossy medium for extractions of inductances and resistances. The frequency dependency of such parameters is also illustrated.
Piecewise affine inverse problems form a general class of nonlinear inverse problems. In particular inverse problems obeying certain variational structures, such as Fermat's principle in travel time tomography, ar...
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Piecewise affine inverse problems form a general class of nonlinear inverse problems. In particular inverse problems obeying certain variational structures, such as Fermat's principle in travel time tomography, are of this type. In a piecewise affine inverse problem a parameter is to be reconstructed when its mapping through a piecewise affine operator is observed, possibly with errors. A piecewise affine operator is defined by partitioning the parameter space and assigning a specific affine operator to each part. A Bayesian approach with a Gaussian random field prior on the parameter space is used. Both problems with a discrete finite partition and a continuous partition of the parameter space are considered. The main result is that the posterior distribution is decomposed into a mixture of truncated Gaussian distributions, and the expression for the mixing distribution is partially analytically tractable. The general framework has, to the authors' knowledge, not previously been published, although the result for the finite partition is generally known. Inverse problems are currently of large interest in many fields. The Bayesian approach is popular and most often highly computer intensive. The posterior distribution is frequently concentrated close to high-dimensional nonlinear spaces, resulting in slow mixing for generic sampling algorithms. Inverse problems are, however, often highly structured. In order to develop efficient sampling algorithms for a problem at hand, the problem structure must be exploited. The decomposition of the posterior distribution that is derived in the current work can be used to develop specialized sampling algorithms. The article contains examples of such sampling algorithms. The proposed algorithms are applicable also for problems with exact observations. This is a case for which generic sampling algorithms tend to fail.
A balanced sampling design is defined by the property that the Horvitz-Thompson estimators of the population totals of a set of auxiliary variables equal the known totals of these variables. Therefore the variances of...
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A balanced sampling design is defined by the property that the Horvitz-Thompson estimators of the population totals of a set of auxiliary variables equal the known totals of these variables. Therefore the variances of estimators of totals of all the variables of interest are reduced, depending on the correlations of these variables with the controlled variables. In this paper, we develop a general method, called the cube method, for selecting approximately balanced samples with equal or unequal inclusion probabilities and any number of auxiliary variables.
This paper proposes a novel sampling algorithm for digital signal processing (DSP) controlled 2 kW power factor correction (PFCs) converters, which can improve switching noise immunity greatly in average-current-contr...
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This paper proposes a novel sampling algorithm for digital signal processing (DSP) controlled 2 kW power factor correction (PFCs) converters, which can improve switching noise immunity greatly in average-current-control power supplies. Based on the newly developed DSP chip TMS320F240, a 2 kW PFC stage is implemented. The novel sampling algorithm shows great advantages when the converter operates at a frequency above 30 kHz.
The best calculation of concentration profiles, isoconcentration surfaces or Gibbsian interfacial excesses from three-dimensional atom-probe microscopy data requires a compromise between spatial positioning error and ...
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The best calculation of concentration profiles, isoconcentration surfaces or Gibbsian interfacial excesses from three-dimensional atom-probe microscopy data requires a compromise between spatial positioning error and statistical sampling error. For example, sampling from larger spatial regions decreases the statistical error, but increases the error in spatial positioning. Finding the appropriate balance for a particular calculation can be tricky, especially when the three-dimensional nature of the data presents an infinite number of degrees of freedom in defining surfaces, and when the statistical error is changing from one region of a sample to another due to differences in collection efficiency or atomic density. We present some strategies for approaching these problems, focusing on efficient algorithms for generating different spatial samplings. We present a unique double-splat algorithm, in which an initial, fine-grained sampling is taken to convert the data to a regular grid, followed by a second, variable width splat, to spread the effective sampling distance to any value,desired. The first sampling is time consuming for a large dataset, but needs only be performed once. The second splat is done on a regular grid, so it is efficient, and can be repeated as many times as necessary to find the correct balance of statistical and positioning error. The net effect is equivalent to a Gaussian spreading of each data point, without the necessity of calculating Gaussian coefficients for millions of data points. We show examples of isoconcentration surfaces calculated under different circumstances from the same dataset. (C) 2002 Published by Elsevier Science B.V.
This paper studies the complexity of the polynomial-time samplable (P-samplable) distributions, which can be approximated within an exponentially small Factor by sampling algorithms in time polynomial in the length of...
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This paper studies the complexity of the polynomial-time samplable (P-samplable) distributions, which can be approximated within an exponentially small Factor by sampling algorithms in time polynomial in the length of their outputs. The paper shows that common assumptions in complexity theory yield the separation of polynomial-time samplable distributions from the polynomial-lime computable distributions with respect to polynomial domination, average-polynomial domination, polynomial equivalence, and average-polynomial equivalence. (C) 1999 Academic Press.
An impedance analyzer is described which used direct sampling of the stimulating and response signals into a laboratory data acquisition system. The analyzer uses subsampling in order to extend the range to frequencie...
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An impedance analyzer is described which used direct sampling of the stimulating and response signals into a laboratory data acquisition system. The analyzer uses subsampling in order to extend the range to frequencies higher than the sampling frequency. An algorithm which computes the optimum sampling rate is described. The analyzer can be used in the frequency range from above 10(5) Hz to below 10(-2) Hz. In the range from 50 kHz to 0.01 Hz the relative amplitude error was found to be less than 0.01% and the phase error to be less than 0.1 degree.
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