We present a unifying approach to discrete Gabor analysis, based on unitary matrix factorization. The factorization point of view is notably useful for the design of efficient numerical algorithms. This presentation is the first systematic account of its kind. In particular, it is shown that differe...
We present a unifying approach to discrete Gabor analysis, based on unitary matrix factorization. The factorization point of view is notably useful for the design of efficient numerical algorithms. This presentation is the first systematic account of its kind. In particular, it is shown that differe...
We give a matrix factorization for the solution of the linear system Ax = f , when coefficient matrix A is a dense symmetric positive definite matrix. We call this factorization as "WW T factorization". The algorithm for this factorization is given. Existence and backward error analysis of the...
This study describes our implementations of two algorithms for performing this factorization, the column Cholesky and the multifrontal methods, based on graph theory applied to sparse symmetric matrices. We use advanced techniques such as loop unrolling and equivalent sparse matrix reordering to improve ...
Numerical algorithms for the computation of an upper bound of the largest structured singular value arising from the A-synthesis control problem are developed. Since the computation for the largest structured singular value has been shown to be an NP-hard problem in literatures, we concentrate the ...
Matrix factorization algorithms QR (qr) LU (lu) Cholesky (chol) Arnoldi iteration (arnoldi) Eigenvalue algorithms QR (eigsQR) QR-Arnoldi (eigsArnoldi) Utilities : Vector and matrix norms, matrix condition number, Givens rotation, Householder reflection ...
All the presented algorithms in the book are illustrated with detailed examples to enable one to write one's own computer code and to understand numerical methods. Volume 1 contains 221 exercises of varying difficulty, distributed approximately uniformly among the seven chapters of the volume. Many ...
(1987). For EM modeling in 3D space, the computational cost of FE increased dramatically. Therefore, with the development of computing power, FE algorithms for 3D EM modeling gained a proficient increase development (Mur1991; Zyserman and Santos2000; Schwarzbach2009; Key and Ovall2011; Schwarz...
A sparse factorization for quasi-Newton type methods has been obtained. Algorithms for solving combined systems of linear and non-linear algebraic equations and matrix splitting have also been developed. A new algorithm has been found for updating the sparse LDU factorization of the approximation to ...
parallel algorithm for GPU; randomized numerical linear algebra; rank-revealing matrix factorization; LINEAR ALGEBRA; RANDOMIZED ALGORITHMS; QR FACTORIZATION; APPROXIMATION; MATRIX; COLUMN; DECOMPOSITION; DIVIDE; 9.Conditioning of hybrid variational data assimilation 机译:混合变分数据同化的调节 作者:Shaerdan...