The generalized Newton iteration for the matrix sign function
Publication
, Journal Article
Sun, X; Quintana-Ortí, ES
Published in: SIAM Journal on Scientific Computing
January 1, 2003
In this paper we present modified algorithms for computing deflating subspaces of matrix pairs using the matrix sign function. Our new algorithms achieve a considerable reduction of the computational cost of the generalized Newton iteration for the matrix sign function and improve the accuracy of the computed deflating subspaces. The matrix sign function is thus revealed as an effective technique for applications in which bases for the deflating subspaces are required. When partial or complete information about the eigenspectrum is desired, the matrix sign function can be used as an initial divide-and-conquer technique. The basic kernels involved in this iteration are especially appropriate for current high-performance architectures.
Duke Scholars
Published In
SIAM Journal on Scientific Computing
DOI
ISSN
1064-8275
Publication Date
January 1, 2003
Volume
24
Issue
2
Start / End Page
669 / 683
Related Subject Headings
- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Sun, X., & Quintana-Ortí, E. S. (2003). The generalized Newton iteration for the matrix sign function. SIAM Journal on Scientific Computing, 24(2), 669–683. https://doi.org/10.1137/S1064827598348696
Sun, X., and E. S. Quintana-Ortí. “The generalized Newton iteration for the matrix sign function.” SIAM Journal on Scientific Computing 24, no. 2 (January 1, 2003): 669–83. https://doi.org/10.1137/S1064827598348696.
Sun X, Quintana-Ortí ES. The generalized Newton iteration for the matrix sign function. SIAM Journal on Scientific Computing. 2003 Jan 1;24(2):669–83.
Sun, X., and E. S. Quintana-Ortí. “The generalized Newton iteration for the matrix sign function.” SIAM Journal on Scientific Computing, vol. 24, no. 2, Jan. 2003, pp. 669–83. Scopus, doi:10.1137/S1064827598348696.
Sun X, Quintana-Ortí ES. The generalized Newton iteration for the matrix sign function. SIAM Journal on Scientific Computing. 2003 Jan 1;24(2):669–683.
Published In
SIAM Journal on Scientific Computing
DOI
ISSN
1064-8275
Publication Date
January 1, 2003
Volume
24
Issue
2
Start / End Page
669 / 683
Related Subject Headings
- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics