11. Bibliography

11.1. Books/articles/proceedings/theses…

[AHLT05] 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. Int. Mr Numer. Meth. Engng, vol. 64, pp204-236 (2005).

[Arn51] W.E. Arnoldi. The principle of minimized iterations in the solution of the matrix eigenvalue problem. Quarter. Call. Math, vol. 9, pp17-19 (1951).

[Bat71] K.J.Bathe*Solution methods for large generalized eigenvalue problems in structural engineering.* Ed. California University Berkeley (1971).

[Ber99] O.Bertrand. Procedures for counting eigenvalues. Thesis from the University of Rennes 1 (1999).

[BDK93] Z.Bai, J.Demmel & A.M. Kenney. On computing condition numbers for the nonsymmetric eigenproblem. ACM transactions on mathematical software, vol 19, pp202-223 (1993).

[BP02] Bergamaschi & Mr. Putti. Numerical comparison of iterative eigensolvers for large symmetric positive definite matrices. Compute. Methods App. Mech. Engrg. 191 5233-5247 (2002).

[Cha88] F.Chatelin. Matrix eigenvalues. Ed. Masson (1988).

[CW85] J.K. Cullum & R.A.Willoughby. Launch algorithms for large symmetric eigenvalue computations. Vol 1 Theory, Ed Birkhäuser (1985).

[DMW71] A.Dubrulle, R.S.Martin & J.H.Wilkinson. The Implicit **QLAlgorithm*. Handbook for automatic computation. Volume 2, Linear Algebra, Springer-Verlag (1971).

[ER80] T.Ericsson & A.Ruhe. The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems. Mathematics of computations, vol. 35, pp1251-1268 (1980).

[GL89] G.H.Golub & C.F.Van Loan. Matrix computations. The Johns Hopkins University Press (1989).

[GSF92] G.Gambolati, F.Sartoretto & P.Florian. An orthogonal accelerated deflation technique for large symmetric eigenproblems. Comp. Meth. Call. Mech. Engrg., 94 13-23 (1992).

[Hau80] Y.Haugazeau. Application of Sylsvester’s theorem to the location of eigenvalues. RAIRO numerical analysis, vol. 14, 1, pp25-41 (1980).

[HRTV07] V.Hernandez, J.E.Roman, A.Tomas & V.Vidal. A survey of software for sparse eigenvalue problems. Report SLEPc available at http://www.grycap.upv.es/slepc.

[Imb91] J.F. Imbert. Analysis of structures by finite elements. Ed. CEPADUES (1991).

[Kny91] A.V. Knyazev. Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method. SIAM J. Sci. Compute., 23 pp517-541 (2001).

[Lan50] C. Lanczos. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. Journal. of research. of the national bureau of standards, vol. 45, no. 4 pp255-282 (1950).

[LS96] R.B.Lehoucq & J.A.Scott. An evaluation of software for computing eigenvalues of sparse nonsymmetric matrices. Argonne National Laboratory Report MCS -P547-1195.

[LT86] P.Lascaux & R.Theodor. Numerical matrix analysis applied to the Art of Engineer. Masson (1986).

[MPW71] R.S.Martin, G.Peters & J.H. Wilkinson. The **QRAlgorithm for Real Hessenberg Matrices*. Handbook for automatic computation,. Vol. 2, Linear Algebra, Springer-Verlag (1971).

[MS73] C.B.Moler & G.W.Stewart. An algorithm for GEP. SIAM J. Num. Anal., 10, 241-256 (1973).

[MS93] R.B.Morgan & D.S.Scott. Preconditioning the Lanczos algorithm for sparse symmetric eigenvalue problems. SIAM J. Sci. Comp, vol. 14 (1993).

[NP77] M.Newmann & A.Pipano. Fast modal extraction in NASTRAN via FEER computer programs, NASTRAN, user manual, NASA Langley Research Center pp485-506 (1977).

[Osb60] E.E.Osborne. On pre-conditioning of matrices. J.Assoc.Comput.Mach., vol. 7, pp338-345 (1960).

[Pai00] C.C.Paige. Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem. Linear Algebra and its Applications, vol. 34 (1980).

[Par80] B.N.Parlett. The symmetric eigenvalue problem. Prentice Hall (1980).

[PR71] B.N.Parlett & C.Reinsch. Balancing a matrix for calculation of eigenvalues and eigenvectors. Handbook for automatic computation. Vol. 2, Linear Algebra, Springer-Verlag (1971).

[Saa80] Y.Saad. On the rates of convergences of the Lanczos and the Block-Lanczos methods. SIAM Mr. Numer. Anal., vol. 17 No. 5, pp687-706 (1980).

Y.Saad. Variation on Arnoldi’s method for computing elements of large unsymetric matrices. Linear Algebra and its Applications, vol. 34, pp269-2395 (1980).

[Saa91] Y.Saad. Numerical methods for large eigenvalue problems. Ed. Manchester University (1991).

[Sad93] Mr. Sadkane. A block Arnoldi-Chebychev method for computing the leading ergenpairs of large sparse unsymmetric matrices. Numerische Mathematik, vol. 64, pp181-193 (1993).

[Sor92] D.C.Sorensen. Implicit applications of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl., vol. 13, pp357-385 (1992).

[SV96] G.L.G.Sleijpen & H.Van der Vorst. A Jacobi-Davidson method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl., 17 pp401-425 (1996).

[TM01] F.Tisser & K.Meerbergen. The quadratic eigenvalue problem. SIAM Review vol. 43, no. 2, pp235-286 (2001).

[Wat07] D.S. Watkins. The matrix has a value problem. SIAM (2007).

[WR71] J.H. Wilkinson & C. Reinsch. Handbook for automatic computation, vol. 2, Linear Algebra, Springer-Verlag (1971).

11.2. Reports/reports EDF

[Beg06] Mr. Begon. Implementation of modal solvers in Code_Aster. INSTN Master Report (2006).

[BQ00] O.Boiteau & B.Quinnez. Spectral analysis method in Code_Aster. Dynamics course booklet available on the website `https://www.code-aster.org`_ < https://www.code-aster.org/> ``_(2000) < https://www.code-aster.org/>.

[Boi08] O.Boiteau. Overview of direct linear solvers and use of product MUMPS. Code_Aster R6.02.03 (2008) Reference Documentation.

[Boi08b] O.Boiteau. Integration of a QZ modal solver into Code_Aster and*Extension of QZ and Sorensen solvers to Code_Aster’s non-symmetric modal problems*. Internal reports EDF R&D CR-I23/2008/030 and CR-I23/2008/044 (2008).

[Boi09] O.Boiteau. Solving the quadratic modal problem (QEP). Code_Aster R5.01.02 (2009) Reference Documentation.

[Boi09b] O.Boiteau. Overview of the conjugate gradient: GCPC Aster and use of the product PETSc. Code_Aster R6.01.02 (2009) Reference Documentation.

[Boi12] O.Boiteau. Procedure for counting eigenvalues. Code_Aster R5.01.04 (2012) Reference Documentation.

[Boy07] E.Boyère. Operator DYNA_TRAN_MODAL. Code_Aster U4.53.21 (2007) User Documentation.

[Pel01] J.Pellet. Dualization of limit conditions. Code_Aster R3.03.01 (2001) Reference Documentation

[Ros07] C.Rose. Multifrontal method. Code_Aster R6.02.02 (2007) Reference Documentation.

[Vau00] J.L. Vaudescal. Introduction to methods for solving large eigenvalue problems. Note EDF R&D HI-72/00/01 (2000)

11.3. Internet resources

[Arp] ARPACK website: `http://www.caam.rice.edu/software/ARPACK < http://www.caam.rice.edu/software/ARPACK /> /`_ ``_ < http://www.caam.rice.edu/software/ARPACK />.

[Lap] LAPACK website: http://www.netlib.org/lapack/.

[MaMA] MatrixMarket website: < http://math.nist.gov/MatrixMarket/index.html>` http://math.nist.gov/MatrixMarket/index.html`_ < http://math.nist.gov/MatrixMarket/index.html>``_.

[Sca] Scalapack website: `http://www.netlib.org/scalapack/`_ < http://www.netlib.org/scalapack/> ``_ < http://www.netlib.org/scalapack/>.