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On the Accuracy of the Element‐wise Jacobi Methods for PGEP
Author(s) -
Matejaš Josip,
Hari Vjeran
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800023
Subject(s) - positive definite matrix , eigenvalues and eigenvectors , transformation (genetics) , element (criminal law) , mathematics , finite element method , approximation error , type (biology) , engineering , physics , structural engineering , ecology , quantum mechanics , biology , political science , law , biochemistry , chemistry , gene
We analyze the relative accuracy of two new element‐wise Jacobi‐type methods for the positive definite generalized eigenvalue problem Ax = λ Bx , where A and B are symmetric matrices and B is positive definite. A detailed error analysis is used, and the appropriate numerical tests are performed. If A and B are well‐behaved positive definite matrices then the transformation parameters will have small relative errors and numerical tests indicate the high relative accuracy of the methods.