Charles Van Loan
Cornell University
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Featured researches published by Charles Van Loan.
Siam Review | 2003
Cleve Moler; Charles Van Loan
In principle, the exponential of a matrix could be computed in many ways. Methods involv- ing approximation theory, dierential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and eciency indicates that some of the methods are preferable to others, but that none are completely satisfactory. Most of this paper was originally published in 1978. An update, with a separate bibliog- raphy, describes a few recent developments.
Siam Review | 1978
Cleve B. Moler; Charles Van Loan
In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polyn...
Archive | 1992
Charles Van Loan
1. The Radix-2 Frameworks. Matrix Notation and Algorithms The FFT Idea The Cooley-Tukey Factorization Weight and Butterfly Computations Bit Reversal and Transposition The Cooley-Tukey Framework The Stockham Autosort Frameworks The Pease Framework Decimation in Frequency and Inverse FFTs 2. General Radix Frameworks. The General Radix Ideas Index Reversal and Transposition Mixed-Radix Factorizations Radix-4 and Radix-8 Frameworks The Split-Radix Frameworks 3. High Performance Frameworks. The Multiple DFT Problem Matrix Transposition The Large Single-Vector FFT Problem Multi-Dimensional FFT Problem Distributed Memory FFTs Shared Memory FFTs 4. Selected Topics. Prime Factor FFTs Convolution FFTs of Real Data Cosine and Sine Transforms Fast Poisson Solvers Bibliography Index.
Journal of Computational and Applied Mathematics | 2000
Charles Van Loan
Abstract The Kronecker product has a rich and very pleasing algebra that supports a wide range of fast, elegant, and practical algorithms. Several trends in scientific computing suggest that this important matrix operation will have an increasingly greater role to play in the future. First, the application areas where Kronecker products abound are all thriving. These include signal processing, image processing, semidefinite programming, and quantum computing. Second, sparse factorizations and Kronecker products are proving to be a very effective way to look at fast linear transforms. Researchers have taken the Kronecker methodology as developed for the fast Fourier transform and used it to build exciting alternatives. Third, as computers get more powerful, researchers are more willing to entertain problems of high dimension and this leads to Kronecker products whenever low-dimension techniques are “tensored” together.
SIAM Journal on Numerical Analysis | 1976
Charles Van Loan
Two generalizations of the singular value decomposition are given. These generalizations provided a unified way of regarding certain matrix problems and the numerical techniques which are used to s...
Archive | 1992
Charles Van Loan; Nikos P. Pitsianis
Let A be an m-by-n matrix with m=m1m2 and n=n1n2. We consider the problem of finding (mathematical formula omitted) so that (mathematical formula omitted) is minimized. This problem can be solved by computing the largest singular value and associated singular vectors of a permuted version of A. If A is symmetric, definite, non-negative, or banded, then the minimizing B and C are similarly structured. The idea of using Kronecker product preconditioners is briefly discussed.
SIAM Journal on Numerical Analysis | 1977
Charles Van Loan
In this paper we examine how the matrix exponential
Linear Algebra and its Applications | 1981
Christopher C. Paige; Charles Van Loan
e^{At}
Linear Algebra and its Applications | 1982
Charles Van Loan
is affected by perturbations in A. Elementary techniques using
ACM Transactions on Mathematical Software | 1998
Bo Kågström; Per Ling; Charles Van Loan
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