Bibliography

1

Axel Ruhe.

Eigenvalues of a complex matrix by the QR-method.
BIT, 6:350-358, 1966.

2

A Ruhe.

On the quadratic convergence of the Jacobi method for normal matrices.
BIT, 7:305-313, 1967.

3

A Ruhe.

On the quadratic convergence of a generalization of the Jacobi method to arbitrary matrices.
BIT, 8:210-231, 1968.

4

A Ruhe.

The norm of a matrix after a similarity transformation.
BIT, 9:53-58, 1969.

5

A Ruhe.

Properties of a matrix with a very ill-conditioned eigenproblem.
Num.Math, 15:57-60, 1970.

6

A Ruhe.

An algorithm for numerical determination of the structure of a general matrix.
BIT, 10:196-216, 1970.

7

A Ruhe.

Perturbation bounds for means of eigenvalues and invariant subspaces.
BIT, 10:343-354, 1970.

8

A Ruhe.

Algorithms for the nonsymmetric algebraic eigenvalue problem.
PhD thesis, Lund University, Lund, Sweden, 1970.

9

A Ruhe.

Algorithms for the nonlinear algebraic eigenvalue problem.
SIAM J. Num. Anal, 10:674-689, 1973.

10

A Ruhe and T Wiberg.

The method of conjugate gradients used in inverse iteration.
BIT, 12:543-554, 1972.

11

A Ruhe.

Iterative eigenvalue algorithms for large symmetric matrices.
In L. Collatz and K. P. Hadeler, editors, Eigenwertprobleme, ISNM 24, volume 24, pages 97-115. Birkhäuser Verlag Basel und Stuttgart, 1974.

12

A Ruhe.

SOR-methods for the eigenvalue problem of large sparse matrices.
Math.Comp, 28:695-710, 1974.

13

A Ruhe.

On the closeness of eigenvalues and singular values for almost normal matrices.
Lin. Alg. Appl., 11:87-93, 1975.

14

A Ruhe.

Iterative eigenvalue algorithms based on convergent splittings.
Journal of Comp. Physics, 19:110-120, 1975.

15

A Ruhe.

Numerical computation of principal components when several observations are missing.
Technical report, UMINF-48, Umeå, 1974.

16

A Ruhe.

Numerical methods for the solution of large sparse eigenvalue problems.
In V.A Barker, editor, Sparse Matrix Techniques, Lect Notes Math 572, pages 130-184. Springer Berlin-Heidelberg-New York, 1976.

17

A Ruhe.

Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse symmetric matrices.
Math. Comp, 33:680-687, 1979.

18

A Ruhe.

Accelerated Gauss-Newton algorithms for nonlinear least squares problems.
BIT, 19:356-367, 1979.

19

A Ruhe and P.Å Wedin.

Algorithms for separable nonlinear least squares problems.
SIAM Review, 22:318-337, 1980.

20

B Kågström and A Ruhe.

An algorithm for numerical computation of the Jordan normal form of a complex matrix.
ACM Trans on Math. Software, 6:398-419 (report) 437-443 (algorithm), 1980.

21

A Ruhe.

The relation between the Jacobi algorithm and inverse iteration and a Jacobi algorithm based on elementary reflections.
BIT, 20:88-96, 1980.

22

A Ruhe.

Eigenvalues in an APL environment, an algorithm based on Rayleigh quotient iteration.
APL Quote Quad 10, 3, pages 29-30, 1980.

23

A Ruhe.

A universal elimination scheme for generalized linear least squares problems with equality constraints.
Technical report, UMINF-74, 1979.

24

A Ruhe.

Fitting empirical data by positive sums of exponentials.
SIAM J. Sci. Stat. Comp., 1:481-498, 1980.

25

A Ruhe.

Fitting empirical data by positive sums of exponentials.
In M.M. Barrit and D. Wishart, editors, COMPSTAT, Edinburgh, pages 622-628. Physica-Verlag, Vienna, 1980.

26

T Ericsson and A Ruhe.

The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems.
Math Comp, 35:1251-1268, 1980.

27

Thomas Ericsson and Axel Ruhe.

STLM - a software package for the spectral transformation Lanczos algorithm.
Technical report, UMINF-101, 1982.

28

Axel Ruhe.

The two-sided Arnoldi algorithm for nonsymmetric eigenvalue problems.
In B. Kågström and A. Ruhe, editors, Matrix Pencils, LNM 973, pages 104-120. Springer-Verlag, Berlin Heidelberg New York, 1983.

29

S. Wold, A. Ruhe, H. Wold, and W.J. Dunn.

The collinearity problem in linear regression. the partial least squares (PLS) approach to generalized inverses.
SIAM J. Sci. Stat. Comp., 5:735-743, 1984.

30

Axel Ruhe.

Numerical aspects of Gram-Schmidt orthogonalization of vectors.
Lin. Alg. Appl., 52/53:591-601, 1983.

31

Axel Ruhe.

Rational Krylov sequence methods for eigenvalue computation.
Lin. Alg. Appl., 58:391-405, 1984.

32

Yong Feng Zhou and Axel Ruhe.

Numerical path following and eigenvalue criteria for branch switching.
In J. Cullum and R.A. Willoughby, editors, Large Scale Eigenvalue Problems, pages 121-142. Elsevier Science Publishers B.V. (North-Holland), 1986.

33

L. Andersson, K. Holmström, and A. Ruhe.

Complex formation constants - a problem from solution chemistry.
In J.C. Mason and M.G. Cox, editors, Algorithms for approximation, pages 557-572. Clarendon Press, Oxford, 1987.

34

Thomas Ericsson and Axel Ruhe.

Lanczos algorithms and field of value rotations for symmetric matrix pencils.
Lin. Alg. Appl., 88/89:733-746, 1987.

35

Axel Ruhe.

Closest normal matrix finally found!
BIT, 27:585-598, 1987. ( Ms with no figures in  normalBIT87.ps  )

36

J. Huitfeldt and A. Ruhe.

A new algorithm for numerical path following applied to an example from hydrodynamical flow.
SIAM J. Sci. Stat. Comp., 11:1181-1192, 1990.

37

Axel Ruhe.

Showing eigenvalues on the Riemann sphere.
In Bo Kågström, editor, Visualization and analysis of scientific and technical computations on high-performance computers, pages 136-141. University of Umeå, Report UMINF-191.90, 1990.

38

Axel Ruhe.

Rational Krylov algorithms for nonsymmetric eigenvalue problems.
In G. Golub, A. Greenbaum, and M. Luskin, editors, Recent Advances in Iterative Methods, IMA Volumes in Mathematics and its Applications 60, pages 149-164. Springer-Verlag, New York, 1994.  RKSima92.ps

39

Axel Ruhe.

Rational Krylov algorithms for nonsymmetric eigenvalue problems, II: Matrix pairs.
Lin. Alg. Appl., 197/198:283-296, 1994.   lissabon.ps

40

Axel Ruhe.

The Rational Krylov algorithm for generalized eigenvalue problems.
In Jiang Er-xiong, editor, Proceedings of '92 Shanghai International Numerical Algebra and its Applications Conference, pages 105-112. China Science and Technology Press, 1994.  shanghai.ps

41

Axel Ruhe.

The Rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices.
BIT, 34:165-176, 1994.  rksr.ps

42

Axel Ruhe.

The Rational Krylov algorithm for large nonsymmetric eigenvalues - mapping the resolvent norms (pseudospectrum).
In Talk given at Sparse Days at St Girons, July 10-16, 1994.  stgirons.ps

43

The Math Works Inc.

Partial Differential Equation Toolbox for use with Matlab, 1995.

44

Axel Ruhe.

Computing nonlinear eigenvalues with spectral transformation Arnoldi.
Z. angew. Math. Mech., 76 S2:17-20, 1996.  Arnzamm.ps

45

Axel Ruhe.

The Rational Krylov for nonlinear eigenvalues.
In Talk at the Householder XIII conference, Pontresina, Switzerland, June 17-21, 1996.  RKSnonl97.ps

46

Axel Ruhe.

Rational Krylov, a practical algorithm for large sparse nonsymmetric matrix pencils.
SIAM J. Sci. Comp., 19:1535-1551, 1998. (Manuscript in  RKSsisc98.ps )

47

Axel Ruhe.

Eigenvalue algorithms with several factorizations - a unified theory yet?
Technical Report 1998:11, Department of Mathematics, Chalmers Univ of Technology, Göteborg, Sweden, 1998.  argonne.ps

48

Axel Ruhe and Daniel Skoogh.

Rational Krylov algorithms for eigenvalue computation and model reduction.
In B. Kågström, , J. Dongarra, E. Elmroth, and J. Wasniewski, editors, Applied Parallel Computing. Large Scale Scientific and Industrial Problems., Lecture Notes in Computer Science, No. 1541, pages 491-502, 1998.  para98.ps

49

Katarina Blom and Axel Ruhe.

Information retrieval with Krylov spaces and Gaussian quadrature.
In Talk at the Householder XIV conference, Whistler Resort, Canada, June 14-18, 1999.  hh99.ps

50

Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, editors.

Templates for the solution of Algebraic Eigenvalue Problems: A Practical Guide.
SIAM, Philadelphia, 2000.

51

Axel Ruhe.

A Rational Krylov algorithm for nonlinear matrix eigenvalue problems
Volume 268 of Zapiski Nauchnyh Seminarov POMI, pages 176-180, 2000: Ruhe268.ps

52

Katarina Blom and Axel Ruhe.

Information retrieval using very short Krylov sequences.
In M.W. Berry, editor, Computational Information Retrieval, volume 106 of Proceedings in Applied Mathematics, pages 41-56. SIAM, Philadelphia, 2001:ruhecir00.ps

53

Katarina Blom and Axel Ruhe.

Information Retrieval using a Krylov subspace method
SIAM Journal on Matrix Analysis and Applications 26:566-582, 2005: 39226-2a.ps
54

Axel Ruhe

Rational Krylov for Large Nonlinear Eigenproblems,
Talk given at PARA 04, Copenhagen June 21, 2004
SPRINGER Lecture Notes in Computer Science, Volume 3732 pp. 357-363, 2006: para04.ps para04.pdf

2006-03-01