References



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References

1
E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen. LAPACK Users' Guide, Release 2.0. SIAM, Philadelphia, 1995. 324 pages. URL http://www.netlib.org/lapack/lug/lapack_lug.html.

2
E. Anderson and J. Dongarra. Results from the initial release of LAPACK. Technical Report LAPACK working note 16, Computer Science Department, University of Tennessee, Knoxville, TN, 1989.

3
E. Anderson and J. Dongarra. Evaluating block algorithm variants in LAPACK. Technical Report LAPACK working note 19, Computer Science Department, University of Tennessee, Knoxville, TN, 1990.

4
Z. Bai. Progress in the numerical solution of the nonsymmetric eigenvalue problem, 1993. To appear in J. Num. Lin. Alg. Appl.

5
Z. Bai and J. Demmel. Design of a parallel nonsymmetric eigenroutine toolbox, Part I. In Proceedings of the Sixth SIAM Conference on Parallel Proceeding for Scientific Computing. SIAM, 1993. Long version available as UC Berkeley Computer Science report all.ps.Z via anonymous ftp from tr-ftp.cs.berkeley.edu, directory pub/tech-reports/csd/csd-92-718.

6
R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, V. Pozo, Romime C., and H. van der Vorst. Templates for the solution of linear systems: Building blocks for iterative methods. SIAM, 1994. URL http://www.netlib.org/templates/templates.ps.

7
R. Boisvert. The architecture of an intelligent virtual mathematical software repository system. Mathematics and Computers in Simulation, 36:269-279, 1994.

8
J. Choi, J. J. Dongarra, R. Pozo, and D. W. Walker. ScaLAPACK: A scalable linear algebra library for distributed memory concurrent computers. In Proceedings of the Fourth Symposium on the Frontiers of Massively Parallel Computation, pages 120-127. IEEE Computer Society Press, 1992.

9
J. Choi, J. J. Dongarra, and D. W. Walker. The design of scalable software libraries for distributed memory concurrent computers. In J. J. Dongarra and B. Tourancheau, editors, Environments and Tools for Parallel Scientific Computing. Elsevier Science Publishers, 1993.

10
D. E. Culler, A. Dusseau, S. C. Goldstein, A. Krishnamurthy, S. Lumetta, T. von Eicken, and K. Yelick. Introduction to Split-C: Version 0.9. Technical report, Computer Science Division - EECS, University of California, Berkeley, CA 94720, February 1993.

11
J. Cullum and R. A. Willoughby. Lanczos algorithms for large symmetric eigenvalue computations. Birkhaüser, Basel, 1985. Vol.1, Theory, Vol.2. Program.

12
J. Demmel. Berkeley Lecture Notes in Numerical Linear Algebra. Mathematics Department, University of California, 1993. 215 pages.

13
J. Demmel and B. Kågström. The generalized Schur decomposition of an arbitrary pencil : Robust software with error bounds and applications. Parts I and II. ACM Trans. Math. Soft., 19(2), June 1993.

14
J. Demmel. LAPACK: A portable linear algebra library for supercomputers. In Proceedings of the 1989 IEEE Control Systems Society Workshop on Computer-Aided Control System Design, December 1989.

15
J. J. Dongarra. Increasing the performance of mathematical software through high-level modularity. In Proc. Sixth Int. Symp. Comp. Methods in Eng. & Applied Sciences, Versailles, France, pages 239-248. North-Holland, 1984.

16
J. J. Dongarra, J. R. Bunch, C. B. Moler and G. W. Stewart. LINPACK Users' Guide. SIAM Press, 1979.

17
J. J. Dongarra. LAPACK Working Note 34: Workshop on the BLACS. Computer Science Dept. Technical Report CS-91-134, University of Tennessee, Knoxville, TN, May 1991.

18
J. J. Dongarra, J. Du Croz, S. Hammarling, and I. Duff. A set of level 3 basic linear algebra subprograms. ACM Transactions on Mathematical Software, 16(1):1-17, 1990.

19
J. J. Dongarra, J. Du Croz, S. Hammarling, and R. Hanson. An extended set of Fortran basic linear algebra subroutines. ACM Transactions on Mathematical Software, 14(1):1-17, March 1988.

20
J. J. Dongarra and R. A. van de Geijn. LAPACK Working Note 37: Two-dimensional basic linear algebra communication subprograms. Computer Science Department, University of Tennessee, Knoxville, TN, October 1991.

21
J. Dongarra and E. Grosse. Distribution of mathematical software via electronic mail. Communications of the ACM, 30(5):403-407, July 1987. URL http://www.netlib.org/.

22
E. W. Felten and S. W. Otto. Coherent parallel C. In G. C. Fox, editor, Proceedings of the Third Conference on Hypercube Concurrent Computers and Applications, pages 440-450. ACM Press, 1988.

23
F. Gantmacher. The Theory of Matrices, Vol. II (transl.). Chelsea, New York, 1959.

24
B. S. Garbow, J. M. Boyle, J. J. Dongarra, and C. B. Moler. Matrix Eigensystem Routines - EISPACK Guide Extension, Volume 51 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1977.

25
G. Golub and C. Van Loan. Matrix Computations. Johns Hopkins University Press, Baltimore, MD, 2nd edition, 1989.

26
R. W. Hockney and C. R. Jesshope. Parallel Computers. Adam Hilger Ltd., Bristol, UK, 1981.

27
T. Kato. Perturbation Theory for Linear Operators. Springer Verlag, Berlin, 2 edition, 1980.

28
C. Lawson, R. Hanson, D. Kincaid, and F. Krogh. Basic Linear Algebra Subprograms for Fortran usage. ACM Trans. Math. Soft., 5:308-323, 1979.

29
A. Packard, M. Fan, and J. Doyle. A power method for the structured singular value. In IEEE Conf. on Decision and Control, pages 2132-2137, 1988.

30
B. Parlett. The Symmetric Eigenvalue Problem. Prentice Hall, Englewood Cliffs, NJ, 1980.

31
B. Parlett. The software scene in the extraction of eigenvalues from sparse matrices. SIAM J. Sci. Stat. Comp., 5:590-604, 1984.

32
W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling. Numerical Recipes in C. Cambridge University Press, Cambridge, UK, 1991.

33
Y. Saad. Numerical methods for large eigenvalue problems. Manchester University Press, 1992.

34
G. Sleijpen and H. van der Vorst. Reliable updated residuals in hybrid Bi-CG methods. Preprint 886, Utrecht University, the Netherlands, 1994. to appear in Computing.

35
G. Sleijpen and H. van der Vorst. A Jacobi-Davidson iteration method for linear eigenvalue problems. Preprint 856 (revised), Utrecht University, the Netherlands, 1995 . to appear in SIMAX.

36
B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, and C. B. Moler. Matrix Eigensystem Routines - EISPACK Guide, Volume 6 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1976.

37
G. W. Stewart. Error and perturbation bounds for subspaces associated with certain eigenvalue problems. SIAM Review, 15(4):727-764, Oct 1973.

38
G. W. Stewart and J.-G. Sun. Matrix Perturbation Theory. Academic Press, New York, 1990.

39
C. Überhuber. Computer-Numerik, Part 1 and 2, Springer Verlag, Berlin, etc, 1995.

40
A.J. van der Steen (ed). Aspects of Computational Science. NCF, Den Haag, the Netherlands, 1995.

41
P. Van Dooren. The computation of Kronecker's canonical form of a singular pencil. Lin. Alg. Appl., 27:103-141, 1979.

42
P. Van Dooren. Reducing subspaces: Definitions, properties and algorithms. In B. Kågström and A. Ruhe, editors, Matrix Pencils, pages 58-73. Springer-Verlag, Berlin, 1983. Lecture Notes in Mathematics, Vol. 973, Proceedings, Pite Havsbad, 1982.

43
J. H. Wilkinson. The Algebraic Eigenvalue Problem. Oxford University Press, Oxford, 1965.

44
J. Wilkinson and C. Reinsch. Handbook for Automatic Computation: Volume II - Linear Algebra. Springer-Verlag, New York, 1971.

45
P. Young, M. Newlin, and J. Doyle. Practical computation of the mixed problem. In Proceedings of the American Control Conference, pages 2190-2194, 1994.



Jack Dongarra
Wed Jun 21 02:35:11 EDT 1995