%ADemmel, J.
%AKahan, W.
%B
%D1988%K99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MATRICES; EIGENVALUES; ALGORITHMS; CONVERGENCE; PERTURBATION THEORY; SYMMETRY; MATHEMATICAL LOGIC
%MOSTI ID: 5039344; Legacy ID: DE88008465
%PMedium: X; Size: Pages: 44
%TComputing small singular values of bidiagonal matrices with guaranteed high relative accuracy: LAPACK working note number 3
%XComputing the singular values of a bidiagonal matrix is the final phase of the standard algorithm for the singular value decomposition of a general matrix. We present a new algorithm which computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magnitudes. In contrast, the standard algorithm for bidiagonal matrices may compute small singular values with no relative accuracy at all. Numerical experiments show that the new algorithm is comparable in speed to the standard algorithm, and frequently faster. We also show how to accurately compute tiny eigenvalues of some classes of symmetric tridiagonal matrices using the same technique. 11 refs., 4 tabs.
%0Technical Report
%@ANL/MCS-TM-110; Other: ON: DE88008465
United StatesOther: ON: DE88008465Wed Feb 06 15:27:41 EST 2008NTIS, PC A03/MF A01; 1.ANL; EDB-88-110542English