References

1

R. Barrett et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia, 1994.

2

M. Berry and G. Golub. Estimating the Largest Singular Values of Large Sparse Matrices via Modified Moments. Numerical Algorithms, 1:353--374, 1991.

3

M. W. Berry. Large scale singular value computations. International Journal of Supercomputer Applications, 6(1):13--49, 1992.

4

M. W. Berry, S. T. Dumais, and G. W. O'Brien. Using linear algebra for intelligent information retrieval. SIAM Review, 37(4):573--595, December 1995.

5

Claude Brezinski. Padé-type approximation and general orthogonal polynomials. Birkhäuser Verlag, 1980.

6

Inc. Cray Research. UNICOS C Library Reference Manual, publication SR-2080. Cray Research, Inc., 655F Lone Oak Drive, Eagan, MN 55121, 5.0 edition, October 1994.

7

J. Dongarra, J. Bunch, C. Moler, and G. W. Stewart. Linpack users' guide. SIAM Philadelphia, 1979.

8

W. Gautschi. On Generating Orthogonal Polynomials. SIAM Journal of Statistical and Scientific Computing, 3(3):289--317, 1982.

9

A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam. PVM: Parallel Virtual Machine. MIT Press, Cambridge, Massachusetts, 1994.

10

G. Golub and M. D. Kent. Estimating Eigenvalues for Iterative Methods. Mathematics of Computation, 53(188):619--626, 1989.

11

G. Golub and C. Van Loan. Matrix Computations. Johns-Hopkins, Baltimore, second edition, 1989.

12

G. Golub, F. T. Luk, and M. L. Overton. A block lanczos method for computing the singular values and corresponding singular vectors of a matrix. ACM Transactions on Mathematical Software, 7(2):149--169, 1981.

13

G. Golub and R. S. Varga. Chebyshev Semi-iterative Methods, Successive Overrelaxation Iterative methods, and Second Order Richardson Iterative Methods. Numerische Mathematik, 3:147--156, 1961.

14

G. H. Golub. Some uses of the lanczos algorithm in numerical linear algebra. In J. Miller, editor, Topics in Numerical Analysis, 1974.

15

A. S. Householder. The Theory of Matrices in Numerical Analysis. Blaisdell, New York, 1964.

16

C. Lanczos. An iteration method for the solution of the eigenvalue problem. J. Res. Nat. Bur. Standards, 45(4):255--282, 1950.

17

R. B. Lehoucq, D. C. Sorensen, and P. Vu. ARPACK: An implementation of the Implicitly Re-started Arnoldi Iteration that computes some of the eigenvalues and eigenvectors of a large sparse matrix. ( Available from netlib@ornl.gov under the directory Scalapack), 1994.

18

C. C. Paige and M. A. Saunders. Solution of sparse indefinite systems of linear equations. SIAM Journal of Numerical Analysis, 12(4):617--629, 1975.

19

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

20

Y. Saad. Numerical Methods For Large Eigenvalue Problems. Manchester University Press, Manchester, UK, 1992.

21

G. W. Stewart. Introduction to Matrix Computations. Academic Press, New York, 1973.

22

S. Varadhan. Estimating the largest singular values/vectors of large sparse matrices via modified moments. Technical Report CS--96--319, University of Tennessee, Knoxville, Tennessee, February 1996.

23

Richard S. Varga. Matrix Iterative Analysis. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1962.