References



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References

1
E. ANDERSON, Z. BAI, C. BISCHOF, J. W. DEMMEL, J. J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, AND D. SORENSEN, LAPACK: A portable linear algebra library for high-performance computers, Computer Science Dept. Technical Report CS-90-105, University of Tennessee, Knoxville, 1990. (LAPACK Working Note 20).

2
E. ANDERSON, Z. BAI, AND J. J. DONGARRA, Generalized QR Factorization and its Applications, Computer Science Dept. Technical Report CS-91-131, University of Tennessee, Knoxville, 1991. (LAPACK Working Note 31).

3
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4
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5
ANSI/IEEE, IEEE Standard for Radix Independent Floating Point Arithmetic, New York, Std 854-1987 ed., 1987.

6
M. ARIOLI, J. W. DEMMEL, AND I. S. DUFF, Solving sparse linear systems with sparse backward error, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 165-190.

7
M. ARIOLI, I. S. DUFF, AND P. P. M. DE RIJK, On the augmented system approach to sparse least squares problems, Num. Math., 55 (1989), pp. 667-684.

8
Z. BAI AND J. W. DEMMEL, On a block implementation of Hessenberg multishift QR iteration, Int. J. of High Speed Comput., 1 (1989), pp. 97-112. (LAPACK Working Note 8).

9
Z. BAI AND J. W. DEMMEL, Design of a parallel nonsymmetric eigenroutine toolbox, Part I, Proceedings of the Sixth SIAM Conference on Parallel Proceesing for Scientific Computing, SIAM (1993), pp. 391-398.

10
Z. BAI AND J. W. DEMMEL, Computing the generalized singular value decomposition, SIAM J. Sci. Comp., 14 (1993), pp. 1464-1486. (LAPACK Working Note 46).

11
Z. BAI, J. W. DEMMEL, AND A. MCKENNEY, On computing condition numbers for the nonsymmetric eigenproblem, ACM Trans. Math. Soft. 19 (1993), pp. 202-223. (LAPACK Working Note 13).

12
Z. BAI AND H. ZHA, A new preprocessing algorithm for the computation of the generalized singular value decomposition, SIAM J. Sci. Comp., 14 (1993), pp. 1007-1012.

13
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14
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15
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16
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17
J. W. DEMMEL, The Condition Number of Equivalence Transformations that Block Diagonalize Matrix Pencils, SIAM J. Num. Anal., 20 (1983), pp. 599-610.

18
J. W. DEMMEL, Underflow and the Reliability of Numerical Software, SIAM J. Sci. Stat. Comput., 5 (1984), pp. 887-919.

19
J. W. DEMMEL AND N. J. HIGHAM, Improved error bounds for underdetermined systems solvers, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 1-14.

20
J. W. DEMMEL AND N. J. HIGHAM, Stability of block algorithms with fast level 3 BLAS, ACM Trans. Math. Soft., 18 (1992), pp. 274-291. (LAPACK Working Note 22).

21
J. W. DEMMEL AND B. KåGSTRÖM, Computing Stable Eigendecompositions of Matrix Pencils, Lin. Alg. Appl., 88/89 (1987), pp. 139-186.

22
J. W. DEMMEL AND W. KAHAN, Accurate singular values of bidiagonal matrices, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 873-912. (LAPACK Working Note 3).

23
J. W. DEMMEL AND X. LI, Faster Numerical Algorithms via Exception Handling, IEEE Trans. Comp., 43 (1994), pp. 983-992. (LAPACK Working Note 59).

24
J. W. DEMMEL AND K. VESELIC, Jacobi's method is more accurate than QR, SIAM J. Matrix Anal. Appl. 13 (1992), pp. 1204-1246. (LAPACK Working Note 15).

25
B. DE MOOR AND P. VAN DOOREN, Generalization of the singular value and QR decompositions, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 993-1014.

26
J. J. DONGARRA, J. R. BUNCH, C. B. MOLER, AND G. W. STEWART, LINPACK Users' Guide, SIAM, Philadelphia, PA, 1979.

27
J. J. DONGARRA, J. DU CROZ, I. S. DUFF, AND S. HAMMARLING, Algorithm 679: A set of Level 3 Basic Linear Algebra Subprograms, ACM Trans. Math. Soft., 16 (1990), pp. 18-28.

28
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29
J. J. DONGARRA, J. DU CROZ, S. HAMMARLING, AND R. J. HANSON, Algorithm 656: An extended set of FORTRAN Basic Linear Algebra Subprograms, ACM Trans. Math. Soft., 14 (1988), pp. 18-32.

30
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31
J. J. DONGARRA, I. S. DUFF, D. C. SORENSEN, AND H. A. VAN DER VORST, Solving Linear Systems on Vector and Shared Memory Computers, SIAM Publications, 1991.

32
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33
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34
J. J. DONGARRA, S. HAMMARLING, AND D. C. SORENSEN, Block reduction of matrices to condensed forms for eigenvalue computations, JCAM, 27 (1989), pp. 215-227. (LAPACK Working Note 2).

35
J. J. DONGARRA AND S. OSTROUCHOV, Quick installation guide for LAPACK on unix systems, Computer Science Dept. Technical Report CS-94-249, University of Tennessee, Knoxville, 1994. (LAPACK Working Note 81).

36
J. J. DONGARRA, R. POZO, AND D. WALKER, An object oriented design for high performance linear algebra on distributed memory architectures, Computer Science Dept. Technical Report CS-93-200, University of Tennessee, Knoxville, 1993. (LAPACK Working Note 61).

37
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38
J. DU CROZ AND N. J. HIGHAM, Stability of methods for matrix inversion, IMA J. Num. Anal., 12 (1992), pp. 1-19. (LAPACK Working Note 27).

39
J. DU CROZ, P. J. D. MAYES, AND G. RADICATI DI BROZOLO, Factorizations of band matrices using Level 3 BLAS, Computer Science Dept. Technical Report CS-90-109, University of Tennessee, Knoxville, 1990. (LAPACK Working Note 21).

40
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41
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42
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43
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44
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45
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46
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47
M. GU AND S. EISENSTAT, A stable algorithm for the rank-1 modification of the symmetric eigenproblem, Yale University, Computer Science Department Report YALEU/DCS/RR-916, New Haven, CT (1992).

48
W. W. HAGER, Condition estimators, SIAM J. Sci. Stat. Comput., 5 (1984), pp. 311-316.

49
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50
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51
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52
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53
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54
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55
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56
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57
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58
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59
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60
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61
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62
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63
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64
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65
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66
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67
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68
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69
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70
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71
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72
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73
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74
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75
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76
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77
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78
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79
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80
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81
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Tue Nov 29 14:03:33 EST 1994