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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.
SIAM, Philadelphia, second edition, 1995.

W. E. Arnoldi.
The principle of minimized iterations in the solution of the matrix eigenvalue problem.
Quart. J. Applied Mathematics, 9:17-29, 1951.

J. Baglama, D. Calvetti, and L. Reichel.
Iterative methods for the computation of a few eigenvalues of a large symmetric matrix.
BIT, 36(3):400-440, 1996.

J. Baglama, D. Calvetti, L. Reichel, and A. Ruttan.
Computation of a few close eigenvalues of a large matrix with application to liquid crystal modeling.
Technical report, Department of Mathematics and Computer Science, Kent State University, 1997.

Z. Bai, J. Demmel, and A. Mckenney.
On computing condition numbers for the nonsymmetric eigenproblem.
ACM Transactions on Mathematical Software, 19(2):202-223, June 1993.

J. Cullum and W. E. Donath.
A block Lanczos algorithm for computing the q algebraically largest eigenvalues and a corresponding eigenspace for large, sparse symmetric matrices.
In Proceedings of the 1974 IEEE Conference on Decision and Control, pages 505-509, New York, 1974.

J. Cullum and R. A. Wilboughby.
Lanczos algorithms for large symmetric eigenvalue computations, volume 1, Theory.
Birkhäuser, Boston, MA., 1985.

J. Cullum and R. A. Willoughby.
Computing eigenvalues of very large symmetric matrices--an implementation of a Lanczos algorithm with no reorthogonalization.
Journal of Computational Physics, 434:329-358, 1981.

J. Daniel, W. B. Gragg, L. Kaufman, and G. W. Stewart.
Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization.
Mathematics of Computation, 30:772-795, 1976.

J. J. Dongarra, J. DuCroz, I. S. Duff, and S. Hammarling.
A set of Level 3 Basic Linear Algebra Subprograms.
ACM Transactions on Mathematical Software, 16(1):1-17, 1990.

J. J. Dongarra, J. DuCroz, S. Hammarling, and R. J. Hanson.
An extended set of Fortran Basic Linear Algebra Subprograms.
ACM Trans. on Math. Software, 14(1):1-17, 1988.

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, Philadelphia, PA., 1991.

T. Ericsson and A. Ruhe.
The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems.
Mathematics of Computation, 35:1251-1268, October 1980.

J. G. F. Francis.
The QR transformation--part 1.
The Computer Journal, 4:265-271, October 1961.

J. G. F. Francis.
The QR transformation--part 2.
The Computer Journal, 4:332-345, January 1962.

G. H. Golub and C. F. Van Loan.
Matrix Computations.
Johns Hopkins University Press, Baltimore, third edition, 1996.

G. H. Golub and R. Underwood.
The block Lanczos method for computing eigenvalues.
In J. R. Rice, editor, Mathematical Software III, pages 361-377. Academic Press, New York, 1977, 1977.

R. G. Grimes, J. G. Lewis, and H. D. Simon.
A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems.
SIAM J. Matrix Analysis and Applications, 15(1):228-272, January 1994.

W. Karush.
An iterative method for finding characteristics vectors of a symmetric matrix.
Pacific J. Mathematics, 1:233-248, 1951.

C. Lanczos.
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators.
J. Research of the National Bureau of Standards, 45(4):255-282, October 1950.
Research Paper 2133.

C. L. Lawson, R. J. Hanson, D. R. Kincaid, and F. T. Krogh.
Basic linear algebra subprograms for Fortran usage.
ACM Transactions on Mathematical Software, 5(3):308-323, 1979.

R. B. Lehoucq.
Analysis and Implementation of an Implicitly Restarted Iteration.
PhD thesis, Rice University, Houston, Texas, May 1995.
Also available as Technical Report TR95-13, Dept. of Computational and Applied Mathematics.

R. B. Lehoucq.
Truncated QR algorithms and the numerical solution of large scale eigenvalue problems.
Preprint MCS-P648-0297, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill, 1997.

R. B. Lehoucq and K. J. Maschhoff.
Implementation of an implicitly restarted block arnoldi method.
Preprint MCS-P649-0297, Argonne National Laboratory, Argonne, Ill, 1997.

R. B. Lehoucq and J. A. Scott.
An evaluation of software for computing eigenvalues of sparse nonsymmetric matrices.
Preprint MCS-P547-1195, Argonne National Laboratory, Argonne, Ill, 1996.

R. B. Lehoucq and D. C. Sorensen.
Deflation techniques for an implicitly restarted Arnoldi iteration.
SIAM J. Matrix Analysis and Applications, 17(4):789-821, October 1996.

T. A. Manteuffel.
Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration.
Numerische Mathematik, 31:183-208, 1978.

R. S. Martin, G. Peters, and J. H. Wilkinson.
The QR algorithm for real Hessenberg matrices.
Numerische Mathematik, 14:219-231, 1978.

K. J. Maschhoff and D. C. Sorensen.
P_ARPACK: An efficient portable large scale eigenvalue package for distributed memory parallel architectures.
In Jerzy Wasniewski, Jack Dongarra, Kaj Madsen, and Dorte Olesen, editors, Applied Parallel Computing in Industrial Problems and Optimization, volume 1184 of Lecture Notes in Computer Science, Berlin, 1996. Springer-Verlag.

K. Meerbergen and D. Roose.
Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems, 1996.

K. Meerbergen and A. Spence.
Implicitly restarted Arnoldi with purification for the shift-invert transformation.
Mathematics of Computation, 218:667-689, 1997.

K. Meerbergen, A. Spence, and D. Roose.
Shift-invert and Cayley transforms for the detection of rightmost eigenvalues of nonsymmetric matrices.
BIT, 34:409-423, 1994.

R. B. Morgan.
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems.
Mathematics of Computation, 65(215):1213-1230, July 1996.

B. Nour-Omid, B. N. Parlett, and Thomas Ericsson Paul S. Jensen.
How to implement the spectral transformation.
Mathematics of Computation, 48(178):663-673, April 1987.

C. C. Paige.
The computation of eigenvalues and eigenvectors of very large sparse matrices.
PhD thesis, University of London, London, England, 1971.

B. N. Parlett.
The Symmetric Eigenvalue Problem.
Prentice-Hall, Englewood Cliffs, N.J., 1980.

B. N. Parlett and J. Reid.
Tracking the progress of the Lanczos algorithm for large symmetric eigenproblems.
IMA Journal of Numerical Analysis, 1:135-155, 1981.

B. N. Parlett and D. Scott.
The Lanczos algorithm with selective orthogonalization.
Mathematics of Computation, 33:217-238, 1979.

Y. Saad.
Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems.
Mathematics of Computation, 42:567-588, 1984.

Y. Saad.
Numerical Methods for Large Eigenvalue Problems.
Halsted Press, 1992.

Y. Saad and M. H. Schultz.
GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems.
SIAM Journal on Scientific and Statistical Computing, 7(3):856-869, July 1986.

I. Schur.
On the characteristic roots of a linear substitution witn an application to the theory of integral equations.
Math. Ann., 66:488-510, 1905.
(in German).

H. Simon.
Analysis of the symmetric Lanczos algorithm with reorthogonalization methods.
Linear Algebra and Its Applications, 61:101-131, 1984.

D. C. Sorensen.
Implicit application of polynomial filters in a k-step Arnoldi method.
SIAM J. Matrix Analysis and Applications, 13(1):357-385, January 1992.

A. Stathopoulos, Y. Saad, and K. Wu.
Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods.
SIAM J. Scientific Computing, 1997.
To appear.

J. M. Varah.
On the separation of two matrices.
SIAM Journal on Numerical Analysis, 16(2):216-222, April 1979.

D. S. Watkins and L. Elsner.
Convergence of algorithms of decomposition type for the eigenvalue problem.
Linear Algebra and Its Applications, 143:19-47, 1991.

J. H. Wilkinson.
The Algebraic Eigenvalue Problem.
Clarendon Press, Oxford, U.K., 1965.

Chao Yang