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Matrix computations (3rd ed.)
Computational Frameworks for the Fast Fourier Transform
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
Nineteen Dubious Ways to Compute the Exponential of a Matrix
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...
Approximation with Kronecker Products
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
An analysis of the total least squares problem
  • G. Golub, C. Loan
  • Mathematics, Computer Science
    Milestones in Matrix Computation
  • 1 February 1980
An algorithm for solving the TLS problem is proposed that utilizes the singular value decomposition and which provides a measure of the underlying problem''s sensitivity.
Generalizing the Singular Value Decomposition
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...
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
Methods involv- ing approximation theory, dierential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed, indicating that some of the methods are preferable to others, but that none are completely satisfactory.
The ubiquitous Kronecker product
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
Computing integrals involving the matrix exponential
A new algorithm for computing integrals involving the matrix exponential is given. The method employs diagonal Pade approximation with scaling and squaring. Rigorous truncation error bounds are given
Matrix Computations, Third Edition