On the Accuracy of the Element‐wise Jacobi Methods for PGEP

Abstract

We analyze the relative accuracy of two new element-wise Jacobi-type methods for the positive definite generalized eigenvalue problem Ax = λBx, 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.