Title :
Error analysis of CORDIC-based Jacobi algorithms
Author :
Paul, Steffen ; Gotze, Jürgen ; Sauer, Matthias
Author_Institution :
Tech. Univ. Munchen, Germany
fDate :
7/1/1995 12:00:00 AM
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;
Journal_Title :
Computers, IEEE Transactions on
