Error analysis of CORDIC-based Jacobi algorithms

Author

Paul, Steffen ; Gotze, Jürgen ; Sauer, Matthias

Author_Institution

Tech. Univ. Munchen, Germany

Volume

44

Issue

7

fYear

1995

fDate

7/1/1995 12:00:00 AM

Firstpage

947

Lastpage

951

Abstract

The Jacobi algorithm for eigenvalue calculation of symmetric matrices can be performed with a CORDIC algorithm as its basic module. Recently, a simplified Jacobi algorithm, by employing approximate rotations based on CORDIC rotations, was proposed. It fully exploits the binary data structure and reduces the overall computational cost significantly. In this paper an error analysis of the approximate CORDIC-based Jacobi algorithm and the conventional CORDIC-based Jacobi algorithm is performed. The new algorithm behaves numerically better than the conventional CORDIC-based Jacobi algorithm for fixed as well as floating point arithmetic

Keywords

Jacobian matrices; computational complexity; eigenvalues and eigenfunctions; error analysis; parallel algorithms; CORDIC; CORDIC rotations; Jacobi algorithms; approximate rotations; binary data structure; computational cost; eigenvalue calculation; error analysis; fixed point arithmetic; floating point arithmetic; symmetric matrices; Computational efficiency; Computer architecture; Data structures; Eigenvalues and eigenfunctions; Error analysis; Floating-point arithmetic; Jacobian matrices; Matrix decomposition; Symmetric matrices; Very large scale integration;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.392855

Filename

392855