Title of article :
Eigen-solving via reduction to DPR1 matrices
Author/Authors :
V.Y. Pan، نويسنده , , B. Murphy، نويسنده , , R.E. Rosholt، نويسنده , , Y. Tang، نويسنده , , X. Wang، نويسنده , , A. Zheng، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2008
Pages :
6
From page :
166
To page :
171
Abstract :
Highly effective polynomial root-finders have been recently designed based on eigen-solving for DPR1 (that is diagonal + rank-one) matrices. We extend these algorithms to eigen-solving for the general matrix by reducing the problem to the case of the DPR1 input via intermediate transition to a TPR1 (that is triangular + rank-one) matrix. Our transforms use substantially fewer arithmetic operations than the QR classical algorithms but employ non-unitary similarity transforms of a TPR1 matrix, whose representation tends to be numerically unstable. We, however, operate with TPR1 matrices implicitly, as with the inverses of Hessenberg matrices. In this way our transform of an input matrix into a similar DPR1 matrix partly avoids numerical stability problems and still substantially decreases arithmetic cost versus the QR algorithm.
Keywords :
The algebraic eigenproblem , DPR1 matrices , TPR1 matrices , Hessenberg matrices
Journal title :
Computers and Mathematics with Applications
Serial Year :
2008
Journal title :
Computers and Mathematics with Applications
Record number :
920905
Link To Document :
بازگشت