Reliable solution of bidiagonal systems with applications

BIT Numerical Mathematics

Volumn 39, Issue 3, 1999, Pages 403-416

  Bar On, Ilan ^a   Leoncini, Mauro ^b,c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b UNIVERSITY OF PISA   (Italy)

^c UNIVERSITY OF FOGGIA   (Italy)

Author keywords

Bidiagonal; Linear systems; Sensitivity analysis; Stable algorithms; Triangular; Tridiagonal

Indexed keywords

EID: 0013003790     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022310417356     Document Type: Article

References (13)

1. I. Bar-On, B. Codenotti, and M. Leoncini, Checking robust nonsingularity of tridiagonal matrices in linear time, BIT, 36 (1996), pp. 206-220.
2. I. Bar-On, B. Codenotti, and M. Leoncini, A fast parallel Cholesky decomposition algorithm for tridiagonal symmetric matrices, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 403-418.
3. I. Bar-On and M. Leoncini, Well defined tridiagonal systems, Manuscript, April 1996. Revised version submitted for publication.
4. I. Bar-On and M. Leoncini, Stable solution of tridiagonal systems, Numerical Algorithms, to appear.
5. I. Bar-On and M. Leoncini, Fast, and reliable parallel solution of bidiagonal systems, LPCR Report #9505, Technion, Israel Institute of Technology, August 1995.
6. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. The Johns Hopkins University Press, Baltimore, MD, 1989.
7. N. J. Higham, Efficient algorithms for computing the condition number of a tridiagonal matrix, SIAM J. Sci. Stat. Comp., 7 (1986), pp. 150-165.
8. N. J. Higham, The accuracy of solutions to triangular systems, SIAM J. Num. Anal., 26 (1989), pp. 1252-1265.
9. N. J. Higham, Algorithm 694: A collection of test matrices in MATLAB, ACM Trans. Math. Software, 17 (1991), pp. 289-305.
10. N. J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, PA, 1995.
11. W. Oettli and W. Prager, Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides, Numer. Math., 6 (1964), pp. 405-409.
12. R. D. Skeel, Scaling for numerical stability in Gaussian elimination, J. Assoc. Comput. Mach, 26 (1979), pp. 494-526.
13. J. H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, 1965.