@string{laa = "Lin. Alg. Appl."}
@string{sissc = "SIAM J. Sci. Stat. Comp."}
@string{sisc = "SIAM J. Sci. Comp."}
@string{etna = "Electronic Trans. Num. Anal."}
@article{r1,
author = {Ruhe, Axel},
title = {Eigenvalues of a complex matrix by the {QR}-method},
journal = {BIT},
volume = {6},
pages = {350-358},
year = {1966},
key = {r1} }
@article{r2,
author = {Ruhe, A},
title = {On the quadratic convergence of the {J}acobi method for normal matrices},
journal = {BIT},
volume = {7},
pages = {305-313},
year = {1967},
key = {r2} }
@article{r3,
author = {Ruhe, A},
title = {On the quadratic convergence of a generalization of the {J}acobi method to arbitrary matrices},
journal = {BIT},
volume = {8},
pages = {210-231},
year = {1968},
key = {r3} }
@article{r4,
author = {Ruhe, A},
title = {The norm of a matrix after a similarity transformation},
journal = {BIT},
volume = {9},
pages = {53-58},
year = {1969},
key = {r4} }
@article{r5,
author = {Ruhe, A},
title = {Properties of a matrix with a very ill-conditioned eigenproblem},
journal = {Num.Math},
volume = {15},
pages = {57-60},
year = {1970},
key = {r5} }
@article{r6,
author = {Ruhe, Axel},
title = {An algorithm for numerical determination of the structure of a general matrix},
journal = {BIT},
volume = {10},
pages = {196-216},
year = {1970},
key = {r6} }
@article{r7,
author = {Ruhe, A},
title = {Perturbation bounds for means of eigenvalues and invariant subspaces},
journal = {BIT},
volume = {10},
pages = {343-354},
year = {1970},
key = {r7} }
@phdthesis{r8,
author = {Ruhe, A},
title = {Algorithms for the nonsymmetric algebraic eigenvalue problem},
journal = {PhD},
year = {1970},
school = {Lund University},
address = {Lund, Sweden},
key = {r8} }
@article{r9,
author = {Ruhe, A},
title = {Algorithms for the nonlinear algebraic eigenvalue problem},
journal = {SIAM J. Num. Anal},
volume = {10},
pages = {674-689},
year = {1973},
key = {r9} }
@article{r10,
author = {Ruhe, A and Wiberg, T},
title = {The method of conjugate gradients used in inverse iteration},
journal = {BIT},
volume = {12},
pages = {543-554},
year = {1972},
key = {r10} }
@inproceedings{r11,
author = {Ruhe, A},
title = {Iterative eigenvalue algorithms for large symmetric matrices},
volume = {24},
pages = {97-115},
year = {1974},
booktitle = {Eigenwertprobleme, ISNM 24},
publisher = {Birkh\"{a}user Verlag Basel und Stuttgart},
editor = {L. Collatz and K. P. Hadeler},
key = {r11} }
@article{r12,
author = {Ruhe, A},
title = {{SOR}-methods for the eigenvalue problem of large sparse matrices},
journal = {Math.Comp},
volume = {28},
pages = {695-710},
year = {1974},
key = {r12} }
@article{r13,
author = {Ruhe, A},
title = {On the closeness of eigenvalues and singular values for almost normal matrices},
journal = {Lin. Alg. Appl.},
volume = {11},
pages = {87-93},
year = {1975},
key = {r13} }
@article{r14,
author = {Ruhe, A},
title = {Iterative eigenvalue algorithms based on convergent splittings},
journal = {Journal of Comp. Physics},
volume = {19},
pages = {110-120},
year = {1975},
key = {r14} }
@article{r15,
author = {Ruhe, A and Wedin, P.\AA{}},
title = {Algorithms for separable nonlinear least squares problems},
journal = {SIAM Review},
volume = {22},
pages = {318-337},
year = {1980},
key = {r15} }
@techreport{r16,
author = {Ruhe, A},
title = {Numerical computation of principal components when several observations are missing},
volume = {48},
year = {1974},
publisher = {Ume\aa{} Universitet},
institution = {UMINF-48},
address = {Ume\aa{}},
key = {r16} }
@article{r18,
author = {K\aa{}gstr\"{o}m, B and Ruhe, A},
title = {An algorithm for numerical computation of the {J}ordan normal form of a complex matrix},
journal = {ACM Trans on Math. Software},
volume = {6},
pages = {398-419 (report) 437-443 (algorithm)},
year = {1980},
key = {r18} }
@inproceedings{Ru76,
author = {Ruhe, A},
title = {Numerical methods for the solution of large sparse eigenvalue problems},
pages = {130-184},
year = {1976},
booktitle = {Sparse Matrix Techniques, Lect Notes Math 572},
publisher = {Springer Berlin-Heidelberg-New York},
editor = {V.A Barker},
key = {r19} }
@article{r20,
author = {Ruhe, A},
title = {Implementation Aspects of Band {L}anczos Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices},
journal = {Math. Comp},
volume = {33},
pages = {680-687},
year = {1979},
key = {r20} }
@article{r21,
author = {Ruhe, A},
title = {Accelerated {G}auss-{N}ewton Algorithms for Nonlinear Least Squares Problems},
journal = {BIT},
volume = {19},
pages = {356-367},
year = {1979},
key = {r21} }
@article{r22,
author = {Ruhe, A},
title = {The Relation Between the {J}acobi Algorithm and Inverse Iteration and a {J}acobi Algorithm Based on Elementary Reflections},
journal = {BIT},
volume = {20},
pages = {88-96},
year = {1980},
key = {r22} }
@article{r23,
author = {Ruhe, A},
title = {Eigenvalues in an {APL} environment, an algorithm based on {R}ayleigh Quotient Iteration},
journal = { {APL} {Q}uote {Q}uad 10, 3},
pages = {29-30},
year = {1980},
key = {r23} }
@techreport{r24,
author = {Ruhe, A},
title = {A universal elimination scheme for generalized linear least squares problems with equality constraints},
volume = {UMINF},
year = {1979},
institution = { UMINF-74},
key = {r24} }
@article{r25,
author = {Ruhe, A},
title = {Fitting empirical data by positive sums of exponentials},
journal = sissc,
volume = {1},
pages = {481-498},
year = {1980},
key = {r25} }
@inproceedings{r26,
author = {Ruhe, A},
title = {Fitting empirical data by positive sums of exponentials},
pages = {622-628},
year = {1980},
booktitle = {COMPSTAT, Edinburgh},
publisher = {Physica-Verlag, Vienna},
editor = {M.M. Barrit and D. Wishart},
key = {r26} }
@article{r27,
author = {Ericsson, T and Ruhe, A},
title = {The spectral Transformation {L}anczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems.},
journal = {Math Comp},
volume = {35},
pages = {1251-1268},
year = {1980},
key = {r27} }
@techreport{r28,
author = {Ruhe, A},
title = {Mathematical Software for Linear Algebra Computations},
pages = {1-15},
year = {1982},
institution = {UMINF-95},
key = {r28} }
@techreport{r29,
author = {Thomas Ericsson and Axel Ruhe},
title = {{STLM} -- a software package for the Spectral Transformation {Lanczos} algorithm},
pages = {1-32},
year = {1982},
institution = {UMINF-101},
key = {r29} }
@inproceedings{Ru82,
author = {Ruhe, Axel},
title = {The Two-sided {A}rnoldi Algorithm for Nonsymmetric Eigenvalue Problems},
pages = {104-120},
year = {1983},
booktitle = {Matrix Pencils, LNM 973},
publisher = {Springer-Verlag, Berlin Heidelberg New York},
editor = {B. K{\aa}gstr\"{o}m and A. Ruhe},
key = {Ru82} }
@article{r31,
author = {S. Wold and A. Ruhe and H. Wold and W.J. Dunn},
title = {The collinearity problem in linear regression. The partial least squares ({PLS}) approach to generalized inverses},
journal = sissc,
volume = {5},
pages = {735-743},
year = {1984},
key = {r31} }
@article{r32,
author = {Ruhe, Axel},
title = {Numerical Aspects of {G}ram-{S}chmidt Orthogonalization of Vectors},
journal = laa,
volume = {52/53},
pages = {591-601},
year = {1983},
key = {r32} }
@inproceedings{Ru83,
author = {Ruhe, Axel},
title = {Rational {K}rylov Sequence Methods for Eigenvalue Computation},
pages = {203-218},
year = {1983},
booktitle = {Vychislitelnie Metody Linejnoj Algebry, Trud' vsjosov konf Moskva August 1982(In Russian)},
publisher = {Akademia Nauk SSSR},
editor = {V. V. Voevodin},
key = {Ru83} }
@article{Ru84,
author = {Ruhe, Axel},
title = {Rational {K}rylov Sequence Methods for Eigenvalue Computation},
journal = laa,
volume = {58},
pages = {391-405},
year = {1984},
publisher = {Elsevier Science Publishing Co.,Inc},
key = {Ru84} }
@inproceedings{r34,
author = {Yong Feng Zhou and Axel Ruhe},
title = {NUMERICAL PATH FOLLOWING AND EIGENVALUE CRITERIA FOR BRANCH SWITCHING},
pages = {121-142},
year = {1986},
booktitle = {Large Scale Eigenvalue Problems},
publisher = {Elsevier Science Publishers B.V. (North-Holland)},
editor = {J. Cullum and R.A. Willoughby},
key = {r34} }
@inproceedings{r35,
author = {L. Andersson and K. Holmstr\"{o}m and A. Ruhe},
title = {Complex formation constants -- a problem from solution chemistry},
pages = {557-572},
year = {1987},
booktitle = {Algorithms for approximation},
publisher = {Clarendon Press, Oxford},
editor = {J.C. Mason and M.G. Cox},
key = {r35} }
@article{r36,
author = {Thomas Ericsson and Axel Ruhe},
title = {{L}anczos Algorithms and Field of Value Rotations for Symmetric Matrix Pencils},
journal = laa,
volume = {88/89},
pages = {733-746},
year = {1987},
key = {r36} }
@article{r37,
author = {Axel Ruhe},
title = {CLOSEST NORMAL MATRIX FINALLY FOUND!},
journal = {BIT},
volume = {27},
pages = {585-598},
year = {1987},
key = {r37} }
@article{HuiR90,
author = {J. Huitfeldt and A. Ruhe},
title = {A new algorithm for numerical path following applied to an example from hydrodynamical flow},
journal = sissc,
volume = {11},
pages = {1181-1192},
year = {1990},
key = {HuiR90} }
@inproceedings{Ru90v,
author = {Ruhe, Axel},
title = {Showing eigenvalues on the {R}iemann sphere},
booktitle= {Visualization and analysis of scientific and technical
computations on high-performance computers},
editor = {Bo K{\aa}gstr{\"o}m},
publisher = {University of Ume\aa, Report UMINF-191.90},
year = {1990},
pages = {136-141}
}
@inproceedings{Ru92m,
author = {Ruhe, Axel},
title = {Rational {K}rylov algorithms for nonsymmetric Eigenvalue problems},
booktitle= {Recent Advances in Iterative Methods,
IMA Volumes in Mathematics and its Applications 60},
editor = {G. Golub and A. Greenbaum and M. Luskin},
publisher = {Springer-Verlag, New York},
year = {1994},
pages = {149-164}
}
@article{Ru92l,
author = {Ruhe, Axel},
title = {Rational {K}rylov algorithms for nonsymmetric Eigenvalue problems,
{II}: Matrix pairs},
journal = laa,
volume = {197/198},
pages = {283-296},
year = {1994}
}
@inproceedings{Ru93s,
author = {Ruhe, Axel},
title = {The {R}ational {K}rylov algorithm for Generalized Eigenvalue problems},
pages = {105-112},
editor = {Jiang Er-xiong},
booktitle= {Proceedings of '92 {S}hanghai International Numerical Algebra and its Applications Conference},
publisher = {China Science and Technology Press},
year = {1994}
}
@article{Ru94f,
author = {Ruhe, Axel},
title = {The {R}ational {K}rylov algorithm for nonsymmetric
Eigenvalue problems. {III}: Complex shifts for real matrices},
journal = {BIT},
volume = {34},
pages = {165-176},
year = {1994}
}
@inproceedings{Ru94g,
author = {Ruhe, Axel},
title = {The {R}ational {K}rylov algorithm for large nonsymmetric
eigenvalues -- mapping the resolvent norms (pseudospectrum)},
booktitle = { Talk given at Sparse Days at St Girons, July 10-16},
year = {1994}
}
@techreport{Ru95b,
author = {Ruhe, Axel},
title = {Rational {K}rylov, a practical algorithm for large sparse
nonsymmetric matrix pencils},
pages = {1-16},
year = {1995},
number = {UCB/CSD-95-871},
institution = {Dept Computer Science, University of California
Berkeley, accepted for publication in SISC}
}
@techreport{RuHT95,
author = {Ruhe, Axel},
title = {Showing the progress of the {R}ational {K}rylov algorithm},
pages = {1-15},
year = {1995},
institution = {Dept Computer Science, University of California
Berkeley, Available as hypertext at
{\tt http://http.cs.berkeley.edu/~ruhe/}}
}
@manual{Ru95m,
title = {Partial Differential Equation Toolbox for
use with Matlab},
organization = {The Math Works Inc.},
year = {1995}
}
@article{Ru95h,
author = {Ruhe, Axel},
title = { Computing nonlinear eigenvalues with spectral
transformation {A}rnoldi},
journal = "Z. angew. Math. Mech.",
volume = "76 S2",
pages = {17-20},
year = {1996}
}
@inproceedings{Ru95t,
author = {Z. Bai and D. Day and J. Demmel and J. Dongarra and
M. Gu and A. Ruhe and H. van der Vorst},
title = {Templates for Linear Algebra Algorithms
},
EDITOR = {Jan van Leeuwen },
BOOKTITLE = { Computer Science Today:
Recent Trends },
SERIES = {Lecture Notes in Computer Science, No. 1000},
YEAR = {1995},
PAGES = {115-140}
}
@inproceedings{Ru96p,
author = {Ruhe, Axel},
title = {The {R}ational {K}rylov for nonlinear
eigenvalues},
booktitle = { Talk at the Householder XIII conference,
Pontresina, Switzerland, June 17-21},
year = {1996}
}
@article{Ru98s,
author = {Ruhe, Axel},
title = {Rational {K}rylov, a practical algorithm for large sparse
nonsymmetric matrix pencils},
journal = sisc,
volume = {19},
pages = {1535-1551},
year = {1998}
}
@techreport{Ru98e,
author = {Ruhe, Axel},
title = {Eigenvalue Algorithms with Several Factorizations --
A Unified Theory yet?},
institution = {Department of Mathematics},
address = {Chalmers Univ of Technology, G{\"o}teborg, Sweden},
number = {1998:11},
year = {1998}
}
@inproceedings{Ru98p,
author = {Ruhe, Axel and Skoogh, Daniel},
title = {Rational {Krylov} Algorithms for Eigenvalue Computation and
Model Reduction},
EDITOR = {K{\aa}gstr{\"{o}}m, B. and Dongarra, J. and Elmroth, E.
and Wa{\'s}niewski, J.},
BOOKTITLE = {Applied Parallel Computing. Large Scale Scientific
and Industrial Problems.},
SERIES = {Lecture Notes in Computer Science, No. 1541},
YEAR = {1998},
PAGES = {491-502}
}
@inproceedings{Ru99h,
author = {Blom, Katarina and Ruhe, Axel},
title = {Information Retrieval with {Krylov} spaces and
{Gaussian} quadrature},
booktitle = { Talk at the Householder XIV conference,
Whistler Resort, Canada, June 14-18},
year = {1999}
}
@inbook{Ru00k,
author = {Axel Ruhe},
title = {A Rational Krylov algorithm for nonlinear
matrix eigenvalue problems},
booktitle = {Numerical Methods and Algorithms. Part
XIV},
series = {Zapiski Nauchnyh Seminarov POMI},
address = {S:t Petersburg},
volume = {268},
editors = {L. Yu. Kolotilina and V. N. Simonova},
pages = {176-180},
year = {2000}
}
@inproceedings{BloRu:01,
author = {Katarina Blom and Axel Ruhe},
title ="Information Retrieval Using Very Short
{Krylov} Sequences",
booktitle = {Computational Information Retrieval},
series = {Proceedings in Applied Mathematics},
volume = {106},
editor = {M.W. Berry},
publisher ={SIAM,
Philadelphia},
year = {2001},
pages = {41-56}
}
@article{BloRu:05,
author = {Katarina Blom and Axel Ruhe},
title ="Information Retrieval using a
{Krylov} subspace method",
year = {2005},
journal ={SIAM Journal on Matrix Analysis and Applications},
volume = {26},
pages = {566-582}
}
@inproceedings{Ru04,
author = {Ruhe, Axel},
title = {Rational {Krylov} for Large Nonlinear Eigenproblems},
EDITOR = {Dongarra, J. and Madsen, K.
and Wa{\'s}niewski, J.},
BOOKTITLE = {Applied Parallel Computing. State of the Art in Scientific Computing},
SERIES = {Lecture Notes in Computer Science, No. 3732},
YEAR = {2006},
PAGES = {357-363}
}
@article{OlRu06,
author = {K. Henrik A. Olsson and Axel Ruhe},
title = {Rational {Krylov} for eigenvalue computation and model order reduction},
journal = {BIT},
volume = {46, Supplement},
pages = {99-111},
year = {2006}
}
@article{Ru10,
author = {Axel Ruhe},
title = {Rational {Krylov} for real pencils with complex eigenvalues},
journal = {Taiwanese Journal of Mathematics},
volume = {14},
pages = {795-803},
year = {2010}
}