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This page describes a range of Jacobi-Davidson literature, including papers that predate the term "Jacobi-Davidson" but contain related ideas.
Entries are sorted alphabetically by their key; where available, links to the papers are given. You will only be able to view these links if your computer/institution is authorized access to the relevant journal. Please let me know if you find a dead link. This bibliography continues to grow. If you know of a relevant paper omitted below, please notify me via m.e.hochstenbach tue.nl.
In many cases, the references below are cross-listed on the Overview and Topics pages; it may be easier to start there.
(Last updated: September 2010)| A |
| [ABG05] | P. Arbenz,
M. Becka,
R. Geus,
U.L. Hetmaniuk
Towards a parallel multilevel preconditioned Maxwell eigensolver. In PARA'04: Workshop on the State-of-the-Art in Scientific Computing, J. Dongarra, K. Madsen, and J. Wasniewski (eds.). Lecture Notes in Computer Science 3732 , pp. 831-838. Springer, Berlin, 2005. Link to preprint |
| [ABG06] | P. Arbenz,
M. Becka,
R. Geus,
U.L. Hetmaniuk,
T. Mengotti
On a parallel multilevel preconditioned Maxwell eigensolver. Parallel Computing 32 (2), pp. 157-165 2006. Link to article |
| [ABG06b] | P.-A. Absil,
C.G. Baker,
K.A. Gallivan
A truncated-CG style method for symmetric generalized eigenvalue problems. J. Comp. Appl. Math. 189, pp. 274-285 2006. Link to article |
| [ACh08] | P. Arbenz,
O. Chinellato
On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices. Appl. Numer. Math. 58 (4), pp. 381-394 2008. Link to article |
| [AGA01] | P. Arbenz,
R. Geus,
S. Adam
Solving Maxwell eigenvalue problems for accelerating cavities. Phys. Rev. ST Accel. Beams 4(2), 2001 Link to article |
| [AGe99] | P. Arbenz,
R. Geus
A comparison of solvers for large eigenvalue problems occurring in the design of resonant cavities. Numer. Linear Algebra Appl. 6(1), pp. 3-16, 1999. Link to article |
| [AGe05] | P. Arbenz,
R. Geus
Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems. Appl. Numer. Math. 54 (2), pp. 107-121, 2005. Link to article |
| [AHL05] | P. Arbenz,
U.L. Hetmaniuk,
R.B. Lehoucq,
R.S. Tuminaro
A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods. Internat. J. Numer. Methods Engrg. 64 (2), pp. 204-236, 2005. Link to article |
| [AHo04] | P. Arbenz,
M.E. Hochstenbach
A Jacobi-Davidson method for solving complex symmetric eigenvalue problems. SIAM J. Sci. Comput. 25(5), pp. 1655-1673, 2004. Link to article |
| [AMS08] | P.-A. Absil,
R. Mahony,
R. Sepulchre
Optimization Algorithms on Matrix Manifolds Princeton University Press, January 2008 Link to book |
| [ASV04] | P.-A. Absil,
R. Sepulchre,
P. Van Dooren,
R. Mahony
Cubically convergent iterations for invariant subspace computation SIAM J. Matrix Anal. Appl. 26 (1), pp. 70-96, 2004. Link to article |
| B |
| [BAG06] | C.G. Baker,
P.-A. Absil,
K.A. Gallivan
An implicit Riemannian trust-region method for the symmetric generalized eigenvalue problem Lecture Notes in Computer Science, Volume 3991 / 2006. Proceedings of the 6th International Conference on Computational Science, Reading, U.K., May 28-31, 2006. Link to article |
| [Bas99] | A. Basermann Parallel Jacobi-Davidson methods with iterative preconditioning for the solution of large sparse Hermitian eigenproblems In Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing 1999 (San Antonio, TX), page 8, Philadelphia, PA, 1999. SIAM. |
| [BDD00] | Z. Bai,
J. Demmel,
J. Dongarra,
A. Ruhe,
H.A. van der Vorst,
editors.
Templates for the Solution of Algebraic Eigenvalue Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000. A practical guide. Link to online book |
| [Bea98] | C. Beattie
Harmonic Ritz and Lehmann bounds. Electr. Trans. Num. Anal. 7, pp. 18-39, 1998. Link to article |
| [BFV96] | A.G.L. Booten, D.R. Fokkema,
G.L.G. Sleijpen,
H.A. van der Vorst
Jacobi-Davidson methods for generalized MHD-eigenvalue problems. Z. Angew. Math. Mech. 76(suppl. 1), pp. 131-134, 1996. Link to article |
| [BNo07] | M. Bollhöfer,
Y. Notay
JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices. Computer Physics Communications 177, pp. 951-964, 2007. Link to article |
| [BPS03] | L. Bergamaschi,
G. Pini,
F. Sartoretto
Computational experience with sequential and parallel, preconditioned Jacobi-Davidson for large, sparse symmetric matrices. J. Comput. Phys. 188(1), pp. 318-331, 2003. Link to article |
| [Bra03a] | J.H. Brandts
The Riccati algorithm for eigenvalues and invariant subspaces of matrices with inexpensive action. Linear Algebra Appl. 358, pp. 335-365, 2003. Link to article |
| [Bra03b] | J.H. Brandts
Solving eigenproblems: from Arnoldi via Jacobi-Davidson to the Riccati method. In Numerical methods and applications, volume 2542 of Lecture Notes in Comput. Sci., pp. 167-173. Springer, Berlin, 2003. Link to article |
| [BSc09] | B. Bandlow,
R. Schuhmann
3-D eigenmode calculation of metallic nano-structures. Adv. Radio Sci. 7, pp. 23-27, 2009. Link to article |
| [BSS09] | M.A. Botchev,
G.L.G. Sleijpen,
A. Sopaheluwakan
An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems. Linear Algebra Appl. 431 (3-4), pp. 427-440, 2009. Link to article |
| [BSS10] | B. Bandlow,
D. Sievers,
R. Schuhmann
An Improved Jacobi-Davidson Method for the Computation of Selected Eigenmodes in Waveguide Cross Sections. IEEE Transactions on Magnetics 46 (8), pp. 3461-3464, 2010. Link to article |
| [BVo04] | T. Betcke,
H. Voss
A Jacobi-Davidson-type projection method for nonlinear eigenvalue problems. Future Generation Computer Systems 20(3), pp. 363-372, 2004. Link to paper Link to preprint |
| C |
| [CAS05] | O. Chinellato,
P. Arbenz,
M. Streiff,
A. Witzig
Computation of optical modes inside axisymmetric open cavity resonators. Future Generation Computer Systems 21 (8), pp. 1263-1274, 2005. Link to article |
| [Chi05] | O. Chinellato
The complex-symmetric Jacobi-Davidson algorithm and its application to the computation of some resonance frequencies of anisotropic lossy axisymmetric cavities. PhD thesis, ETH Zurich, 2005. Link to thesis |
| [CHL02] | M.T. Chu,
T.-M. Huang,
W.-W. Lin
A Novel Deflation Technique for Solving Quadratic Eigenvalue Problems. Preprint, 2002. Link to preprint |
| D |
| [Dav75] | E.R. Davidson
The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comput. Phys. 17, pp. 87-94, 1975. |
| [DGh05] | H.A. Dijkstra,
M. Ghil
Low-frequency variability of the ocean circulation: a dynamical systems approach. Reviews of Geophysics 43, RG3002, doi:10.1029/2002RG000122, (2005). Link to preprint |
| [Dij05] | H.A. Dijkstra
Nonlinear Physical Oceanography: A Dynamical Systems Approach to the Large Scale Ocean Circulation and El Niño 2nd Revised and Enlarged Edition Series: Atmospheric and Oceanographic Sciences Library , Vol. 28 2nd rev. and enlarged ed., 2005, XVI, 532 p., Hardcover ISBN: 978-1-4020-2262-3 |
| [Dij06] | H.A. Dijkstra
On the interaction of SST modes in the North Atlantic Ocean J. Physical Oceanography 36, pp. 286-299, 2006. Link to preprint |
| [DMW83] | J. Dongarra, C.B. Moler, J.H. Wilkinson
Improving the accuracy of computed eigenvalues and eigenvectors. SIAM J. Numer. Anal. 20(1), pp. 23-45, 1983. Link to article |
| [Don83] | J. Dongarra
Improving the accuracy of computed singular values. SIAM J. Sci. Stat. Comput. 4(4), pp. 712-719, 1983. Link to article |
| [Dor97] | J.L.M. van Dorsselaer
Computing eigenvalues occurring in continuation methods with the Jacobi-Davidson QZ method. J. Comput. Phys. 138(2), pp. 714-733, 1997. Link to article Link to preprint |
| [DOW01] | H.A. Dijkstra,
H. Oksuzoglu,
F.W. Wubs,
E.F.F.A. Botta
A fully implicit model of the three-dimensional thermohaline ocean circulation J. Comp. Physics 176, 685-715, 2001. Link to preprint |
| [Dum07] | N.A. Dumont
On the solution of generalized non-linear complex-symmetric eigenvalue problems. Internat. J. Numer. Methods Engrg. 71 (13), pp. 1534-1568, 2007. Link to article |
| E |
| [EAS98] | A. Edelman,
T.A. Arias,
S.T. Smith
The geometry of algorithms with orthogonality constraints SIAM J. Matrix Anal. Appl. 20(2), pp. 303-353, 1998. Link to article |
| [Esh02] | J. van den Eshof
The convergence of Jacobi-Davidson iterations for Hermitian eigenproblems. Numer. Linear Algebra Appl. 9(2), pp. 163-179, 2002. Link to article |
| F |
| [Fen01] | Y.T. Feng
An integrated Davidson and multigrid solution approach for very large scale symmetric eigenvalue problems. Comput. Methods Appl. Mech. Engrg. 190(28), pp. 3543-3563, 2001. Link to article |
| [FJi05] | S. Feng,
Z. Jia
A refined Jacobi-Davidson method and its correction equation. Comput. Math. Appl. 49(2-3), pp. 417-427, 2005. Link to article |
| [FSp07] | M. Freitag,
A. Spence
Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem. Electr. Trans. Num. Anal. 28, pp. 40-64, 2007. Link to article |
| [FSp08] | M. Freitag,
A. Spence
Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves. Linear Algebra Appl. 428 (8-9), pp. 2049-2060, 2008. Link to article |
| [FSV98a] | D.R. Fokkema,
G.L.G. Sleijpen,
H.A. van der Vorst
Accelerated inexact Newton schemes for large systems of nonlinear equations. SIAM J. Sci. Comput. 19(2), pp. 657-674, 1998. Link to article |
| [FSV98b] | D.R. Fokkema,
G.L.G. Sleijpen,
H.A. van der Vorst
Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils. SIAM J. Sci. Comput. 20(1), pp. 94-125, 1998. Link to article |
| G |
| [Geu02] | R. Geus
The Jacobi-Davidson algorithm for solving large sparse symmetric eigenvalue problems with application to the design of accelerator cavities. PhD thesis no. 14734, ETH Zurich, 2002. Link to thesis |
| [GSl99] | M. Genseberger,
G.L.G. Sleijpen Alternative correction equations in the Jacobi-Davidson method Numer. Linear Algebra Appl. 6(3), pp. 235-253, 1999. Link to article |
| [GSV00] | M. Genseberger,
G.L.G. Sleijpen,
H.A. van der Vorst
Using domain decomposition in the Jacobi-Davidson method. Preprint 1164, Department of Mathematics, Utrecht University, October 2000. Link to preprint |
| [GSV03] | M. Genseberger,
G.L.G. Sleijpen,
H.A. van der Vorst
An optimized Schwarz method in the Jacobi-Davidson method for eigenvalue problems. In Domain decomposition methods in science and engineering, pages 289-296. Natl. Auton. Univ. Mex., Mexico, 2003. |
| H |
| [HBe00] | V. Heuveline,
C. Bertsch.
On multigrid methods for the eigenvalue computation of nonselfadjoint elliptic operators. East-West J. Numer. Math. 8(4), pp. 275-297, 2000. |
| [Hec07] | G. Hechme
Convergence analysis of the Jacobi-Davidson method applied to a generalized eigenproblem. C. R. Math. Acad. Sci. Paris 345 (5), pp 293-296, 2007. Link to article |
| [HGe98] | R.S. Heeg, B.J. Geurts
Spatial instabilities of the incompressible attachment-line flow using sparse matrix Jacobi-Davidson techniques. Appl. Sci. Res. 59(4), pp. 315-329, 1998. Link to article |
| [HKP05] | M.E. Hochstenbach,
T. Kosir,
B. Plestenjak
A Jacobi-Davidson type method for the nonsingular two-parameter eigenvalue problem. SIAM J. Matrix Anal. Appl. 26(2), pp. 477-497, 2005. Link to article |
| [HLe07] | U.L. Hetmaniuk,
R.B. Lehoucq
Multilevel Methods for Eigenspace Computations in Structural Dynamics. In: Domain Decomposition Methods in Science and Engineering XVI, Lecture Notes in Computational Science and Engineering, 2007, Volume 55, Part I, pp. 103-113, 2007. Link to article |
| [HLL05] | T.-M. Huang,
W.-W. Lin,
J.-L. Liu ,
W. Wang
Jacobi-Davidson methods for cubic eigenvalue problems. Numer. Linear Algebra Appl. 12, 585-682, 2005. Link to article |
| [HLM03] | T.-M. Huang,
W.-W. Lin,
V. Mehrmann
Numerical solution of quadratic eigenvalue problems with structure-preserving methods. SIAM J. Sci. Comput. 24(4), pp. 1283-1302, 2003. Link to article |
| [HLo09] | M. Hochbruck,
D. Löchel
A multilevel Jacobi-Davidson method for polynomial pde eigenvalue problems arising in plasma physics. To appear in SIAM J. Sci. Comput.. Link to preprint |
| [HLW04] | T.-M. Huang,
W.-W. Lin,
W.-C. Wang,
W. Wang
Numerical simulation of three dimensional pyramid quantum dot. J. Comput. Phys. 196(1), pp. 208-232, 2004. Link to article |
| [HNo06] | M.E. Hochstenbach,
Y. Notay
The Jacobi-Davidson method. GAMM Mitteilungen 29(2), pp. 368-382, 2006. Link to preprint |
| [HNo07] | M.E. Hochstenbach,
Y. Notay
Homogeneous Jacobi-Davidson. Electr. Trans. Num. Anal. 29, pp. 19-30, 2007. Link to article |
| [HNo09] | M.E. Hochstenbach,
Y. Notay
Controlling inner iterations in the Jacobi-Davidson method. SIAM. J. Matrix Anal. Appl. 31(2), pp. 460-477, 2009. Link to article |
| [HNS08] | G. Hechme,
Y.M. Nechepurenko, M. Sadkane
Efficient methods for computing spectral projectors for linearized hydrodynamic equations. SIAM J. Sci. Comput. 31 (1), pp 667-686, 2008. Link to article |
| [Hoc01] | M.E. Hochstenbach
A Jacobi-Davidson type SVD method. SIAM J. Sci. Comput. 23(2), pp. 606-628, 2001. Link to article |
| [Hoc04] | M.E. Hochstenbach
Harmonic and refined extraction methods for the singular value problem, with applications in least squares problems. BIT 44(4), pp. 721-754, 2004. Link to article |
| [Hoc05] | M.E. Hochstenbach
Generalizations of harmonic and refined Rayleigh-Ritz. Electr. Trans. Num. Anal. 20, pp. 235-252, 2005. Link to article |
| [Hoc08] | M.E. Hochstenbach
A Jacobi-Davidson type method for the product eigenvalue problem. J. Comp. Appl. Math. 212 (1), pp. 46-62, 2008. Link to article |
| [Hoc09] | M.E. Hochstenbach
A Jacobi-Davidson type method for the generalized singular value problem. Linear Algebra Appl. 431 (3-4), pp. 471-487, 2009. Link to article |
| [Hocpp] | M.E. Hochstenbach
Variations on harmonic Rayleigh-Ritz for standard and generalized eigenproblems. Preprint. Link to preprint |
| [HPl02] | M.E. Hochstenbach,
B. Plestenjak
A Jacobi-Davidson type method for a right definite two-parameter eigenvalue problem. SIAM J. Matrix Anal. Appl. 24(2), pp. 392-410, 2002. Link to article |
| [HSl03] | M.E. Hochstenbach,
G.L.G. Sleijpen
Two-sided and alternating Jacobi-Davidson. Linear Algebra Appl. 358(1-3), pp. 145-172, 2003. Link to article |
| [HSl08] | M.E. Hochstenbach,
G.L.G. Sleijpen
Harmonic and refined Rayleigh-Ritz for the polynomial eigenvalue problem. Num. Lin. Alg. Appl. 15(1), pp. 35-54, 2008. Link to article |
| [HWH10] | F.-N. Hwang,
ZH Wei,
T.-M. Huang,
W. Wang
A parallel additive Schwarz preconditioned Jacobi-Davidson algorithm for polynomial eigenvalue problems in quantum dot simulation. J. Comput. Phys. 229 (8), 2932-2947, 2010. Link to article |
| J |
| [Jac45] | C.G.J. Jacobi
Über eine neue Auflösungsart der bei der Methode der kleinsten Quadrate vorkommende linearen Gleichungen. Astronom. Nachr., pp. 297-306, 1845. |
| [Jac46] | C.G.J. Jacobi
Über ein leichtes Verfahren, die in der Theorie der Säcularstörungen vorkommenden Gleichungen numerisch aufzulösen. J. Reine und Angew. Math., pp. 51-94, 1846. |
| [Jia97] | Z. Jia
Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems. Linear Algebra Appl. 259, pp. 1-23, 1997. Link to article |
| [JWa09] | Z. Jia,
W. Zeng
A convergence analysis of the inexact Rayleigh quotient iteration and simplified Jacobi-Davidson method for the large Hermitian matrix eigenproblem. Sci. China Ser. A 51 (12), pp. 2205--2216, 2009. Link to preprint |
| K |
| [Kue10] | P. Kürschner
Two-Sided Eigenvalue Methods for Modal Approximation Master thesis, Chemnitz University of Technology; 2010. Link to thesis |
| L |
| [LEl02] | E. Lundström,
L. Eldén
Adaptive eigenvalue computations using Newton's method on the Grassmann manifold SIAM. J. Matrix Anal. Appl. 23(3), pp. 819-839, 2002. Link to article |
| [LLe99] | C. Liu,
J.-F. Lee
Jacobi-Davidson algorithm and its application to modeling RF/microwave detection circuits. Comput. Methods Appl. Mech. Engrg. 169(3-4), pp. 359-375, 1999. Link to article |
| [LMe99] | R.B. Lehoucq,
K. Meerbergen
Using generalized Cayley transformations within an inexact rational Krylov sequence method. SIAM J. Matrix Anal. Appl. 20(1), pp. 131-148, 1999. Link to article |
| [Loc09] | D. Löchel
Numerical methods for eigenvalue problems in the description of drift instabilities in the plasma edge. Phd thesis, Heinrich Heine Universität Düsseldorf, 2009. Link to thesis |
| M |
| [Mee00] | K. Meerbergen
Locking and restarting quadratic eigenvalue solvers. SIAM J. Sci. Comput. 22(5), pp. 1814-1839, 2000. Link to article |
| [Mor91] | R.B. Morgan
Computing interior eigenvalues of large matrices. Linear Algebra Appl. 154/156, pp. 289-309, 1991. Link to article |
| [Mor00] | R.B. Morgan
Preconditioning eigenvalues and some comparison of solvers. J. Comput. Appl. Math. 123(1-2), pp. 101-115, 2000. Numerical analysis 2000, Vol. III. Linear algebra. Link to article |
| [MVo04] | V. Mehrmann,
H. Voss
Nonlinear eigenvalue problems: A challenge for modern eigenvalue methods. GAMM Mitteilungen 27, pp. 121-152, 2004. Link to preprint |
| N |
| [NHI08] | P. Nickel, V. Hill, P. Ingelström, R. Dyczij-Edlinger
A Jacobi-Davidson Method for the hp Multilevel Analysis of Cavity Modes. Electromagnetics, 28 (1), pp. 92-108, 2008. Link to article |
| [NRo07] | T.L. van Noorden,
J. Rommes
Computing a partial generalized real Schur form using the Jacobi-Davidson method. Numer. Linear Algebra Appl. 14 (3), 197-215, 2007. Link to article |
| [Not02] | Y. Notay
Combination of Jacobi-Davidson and conjugate gradients for the partial symmetric eigenproblem. Numer. Lin. Alg. Appl. 9, pp. 21-44, 2002. Link to article |
| [Not03] | Y. Notay
Convergence analysis of inexact Rayleigh quotient iteration. SIAM J. Matrix Anal. Appl. 24, pp. 627-644, 2003. Link to article |
| [Not05] | Y. Notay
Is Jacobi-Davidson faster than Davidson? SIAM J. Matrix Anal. Appl. 26(2), pp. 522-543, 2004/05. Link to article |
| [NPl99] | M. Nool, A. van der Ploeg
Parallel Jacobi-Davidson for solving generalized eigenvalue problems. In Vector and parallel processing-VECPAR '98 (Porto), volume 1573 of Lecture Notes in Comput. Sci., pp. 58-70. Springer, Berlin, 1999. Link to article |
| [NPl00] | M. Nool, A. van der Ploeg
A parallel Jacobi-Davidson-type method for solving large generalized eigenvalue problems in magnetohydrodynamics. SIAM J. Sci. Comput. 22(1), pp. 95-112, 2000. Link to article |
| O |
| [Ovt03a] | E. Ovtchinnikov
Convergence estimates for the generalized Davidson method for symmetric eigenvalue problems. I. The preconditioning aspect. SIAM J. Numer. Anal. 41(1), pp. 258-271, 2003. Link to article |
| [Ovt03b] | E. Ovtchinnikov
Convergence estimates for the generalized Davidson method for symmetric eigenvalue problems. II. The subspace acceleration. SIAM J. Numer. Anal. 41(1), pp. 272-286, 2003. Link to article |
| P |
| [PPV95] | C.C. Paige,
B.N. Parlett,
H.A. van der Vorst
Approximate solutions and eigenvalue bounds from Krylov subspaces. Num. Lin. Alg. Appl. 2(2), pp. 115-133, 1995. |
| R |
| [RBV04] | J. Rommes, W. Bomhof,
H.A. van der Vorst, E.J.W. ter Maten
The application of preconditioned Jacobi-Davidson methods in pole-zero analysis. In Scientific Computing in Electrical Engineering (2004), W.H.A. Schilders, E.J.W. ter Maten, S.H.M.J. Houben, Ed., Mathematics in Industry, Springer. Link to preprint |
| [Rom02] | J. Rommes
Jacobi-Davidson methods and preconditioning with applications in pole-zero analysis. Master's thesis, Utrecht University, June 2002. Link to thesis |
| [Rom07] | J. Rommes
Methods for eigenvalue problems with applications in model order reduction. PhD thesis, Utrecht University, 2007. Link to thesis |
| [Rom08] | J. Rommes
Arnoldi and Jacobi-Davidson methods for generalized eigenvalue problems $Ax=\lambda Bx$ with singular $B$. Math. Comp. 77 (262), pp. 995-1015, 2008. Link to preprint |
| [RTK15] | M. Röhrig-Zöllner, J. Thies, M. Kreutzer, A. Alvermann, A. Pieper, A. Basermann, G. Hager, G. Wellein, H. Fehske
Increasing the Performance of the Jacobi-Davidson Method by Blocking. SIAM J. Sci. Comp. 37 (6), pp. C697-C722, 2015. Link to article |
| [RVM04] | J. Rommes,
H.A. van der Vorst, E.J.W. ter Maten
Jacobi-Davidson methods and preconditioning with applications in pole-zero analysis. In Progress in industrial mathematics at ECMI 2002, volume 5 of Math. Ind., pp. 191-196. Springer, Berlin, 2004. Link to preprint |
| S |
| [SBF96] | G.L.G. Sleijpen, A.G.L. Booten, D.R. Fokkema,
H.A. van der Vorst
Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT 36(3), pp. 595-633, 1996. Link to article |
| [Sch08] | K. Schreiber
Nonlinear Eigenvalue Problems: Newton-type Methods and Nonlinear Rayleigh Functionals. Phd thesis, TU Berlin, 2008. Link to thesis |
| [SEl02] | V. Simoncini,
L. Eldén
Inexact Rayleigh quotient-type methods for eigenvalue computations. BIT 42, pp. 159-182, 2002. Link to article |
| [SEs03] | G.L.G. Sleijpen,
J. van den Eshof
On the use of harmonic Ritz pairs in approximating internal eigenpairs Lin. Alg. Appl. 358(1-3), pp. 115-137, 2003. Link to article |
| [Sor02] | D.C. Sorensen
Numerical methods for large eigenvalue problems. Acta Numerica 11, pp. 519-584, 2002. Link to article |
| [SSa98] | A. Stathopoulos,
Y. Saad
Restarting techniques for the (Jacobi-)Davidson symmetric eigenvalue methods. Electron. Trans. Numer. Anal. 7, pp. 163-181, 1998. Link to article |
| [SSc06] | K. Schreiber,
H. Schwetlick
A primal-dual Jacobi-Davidson-like method for nonlinear eigenvalue problems. Preprint October 2006. Link to preprint |
| [SSc07] | K. Schreiber,
H. Schwetlick
A Jacobi-Davidson like method for nonlinear eigenvalue problems based on singularity theory. PAMM, Proc. Appl. Math. Mech. 7, 2007. Link to article |
| [Sta02] | A. Stathopoulos
A case for a biorthogonal Jacobi-Davidson method: restarting and correction equation. SIAM J. Matrix Anal. Appl. 24(1), pp. 238-259, 2002. Link to article |
| [Sta07a] | A. Stathopoulos
Nearly optimal preconditioned methods for Hermitian eigenproblems under limited memory. Part I: Seeking one eigenvalue. SIAM J. Sci. Comput. 29 (2), pp. 481-514, 2007. Link to article |
| [Sta07b] | A. Stathopoulos
Nearly optimal preconditioned methods for Hermitian eigenproblems under limited memory. Part II: Seeking many eigenvalues. SIAM J. Sci. Comput. 29 (5), pp. 2162-2188, 2007. Link to article |
| [Ste01] | G.W. Stewart
Matrix algorithms. Vol. II. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2001. |
| [STo00] | A. Sameh, Z. Tong
The trace minimization method for the symmetric generalized eigenvalue problem J. Comput. Appl. Math. 123(1-2), pp. 155-175, 2000. Numerical analysis 2000, Vol. III. Linear algebra. Link to article |
| [Stu98] | E. de Sturler
Variations on the Jacobi-Davidson theme. In D. Kincaid and A. Elster, editors: Iterative Methods in Scientific Computation IV: Proceedings of the Fourth IMACS International Symposium on Iterative Methods in Scientific Computation, Austin, Texas, October 18-20, 1998, IMACS series in Computational and Applied Mathematics, volume 5, IMACS 1999, pp. 313-323. Link to preprint |
| [Stu02] | E. de Sturler
Improving the convergence of the Jacobi-Davidson algorithm. Preprint, Department of Computer Science, University of Illinois at Urbana-Champaign, 2002. Link to preprint |
| [SVG96] | G.L.G. Sleijpen,
H.A. van der Vorst,
M. van Gijzen
Quadratic eigenproblems are no problem. SIAM News 8:9-10, September 1996. Link to preprint |
| [SVo96] | G.L.G. Sleijpen,
H.A. van der Vorst
A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl. 17(2), pp. 401-425, 1996. Link to article |
| [SVo96b] | G.L.G. Sleijpen,
H.A. van der Vorst
The Jacobi-Davidson method for eigenvalue problems and its relation with accelerated inexact Newton schemes. In S.D. Margenov and P.S. Vassilevski, editors, Iterative Methods in Linear Algebra, II., volume 3 of IMACS Series in Computational and Applied Mathematics, pp. 377-389, New Brunswick, NJ, U.S.A., 1996. IMACS. Link to preprint |
| [SVo00] | G.L.G. Sleijpen,
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