Accuracy of two SVD algorithms for 2×2 triangular matrices

摘要

A new algorithm for the accurate computation of the singular value decomposition of 2×2 triangular matrices is proposed. The algorithm is based on Voevodin formulas. Sharp accuracy bounds are derived by using a subtle error analysis which tracks the signs of the errors of intermediate quantities and does not neglect the non-linear parts of the errors. The analysis is fine tuned for the case of almost diagonal matrices. The same analysis is also used to analyze the errors for the xLASV2 computational routine of LAPACK. The error estimates of the new algorithm compare favorably to those of the LAPACK routine.