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… Expand

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...

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… Expand

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.Expand

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...

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.Expand

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… Expand

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… Expand