Algorithm 694: a collection of test matrices in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Stability of block algorithms with fast level-3 BLAS
ACM Transactions on Mathematical Software (TOMS)
Matrix computations (3rd ed.)
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Applied Numerical Analysis Using MATLAB
Applied Numerical Analysis Using MATLAB
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
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Recently Golub and Yuan [BIT 42 (2002) 814] proposed the ST decomposition for matrices. However, its numerical stability has not been discussed so far. Here we present preliminary investigations on the numerical behavior of the ST decomposition. We also propose modifications (modified algorithm) to improve the algorithm's numerical stability. Numerical tests of the Golub-Yuan algorithm and our modified algorithm are given for some famous test matrices. All tests include comparisons with the LU (or Cholesky) decomposition without pivoting. These numerical tests indicate that the Golub-Yuan algorithm and its modified version possess reasonable numerical stability. In particular, the modified algorithm is stable for sparse matrices. Moreover, it is more stable than the Golub-Yuan algorithm in the case of dense matrices.