Page 81 - Textos de Matemática Vol. 44

FIELD OF VALUES OF A MATRIX INVERSE 71
[4] M. E. Hochstenbach, Fields of values and inclusion regions for matrix pencils, Electron. Trans. Numer. Anal. 38 (2011), 98–112.
[5] M. E. Hochstenbach and Y. Notay, The Jacobi–Davidson method., GAMM Mitteilungen 29 (2006), 368–382.
[6] M. E. Hochstenbach, D. A. Singer, and P. F. Zachlin, Eigenvalue inclusion regions from inverses of shifted matrices, Linear Algebra Appl. 429 (2008), 2481–2496.
[7] C. R. Johnson, Numerical determination of the field of values of a general complex matrix, SIAM J. Numer. Anal. 15 (1978), 595–602.
[8] T. A. Manteuffel and G. Starke, On hybrid iterative methods for nonsymmetric systems of linear equations, Numer. Math. 73 (1996), 489–506.
[9] The Matrix Market. http://math.nist.gov/MatrixMarket, a repository for test matri- ces.
[10] C.C.Paige,B.N.Parlett,andH.A.vanderVorst,Approximatesolutionsandeigenvalue bounds from Krylov subspaces, Num. Lin. Alg. Appl. 2 (1995), 115–133.
[11] V. Simoncini and D. B. Szyld, Interpreting IDR as a Petrov-Galerkin method, SIAM J. Sci. Comput. 32 (2010), 1898–1912.
[12] G. L. G. Sleijpen and H. A. van der Vorst, A Jacobi–Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (1996), 401–425.
[13] G. W. Stewart, Matrix Algorithms. Vol. II, Society for Industrial and Applied Mathe- matics (SIAM), Philadelphia, PA, 2001.
[14] L. N. Trefethen and M. Embree, Spectra and Pseudospectra, Princeton University Press, Princeton, NJ, 2005.
[15] H. A. van der Vorst, Iterative Krylov Methods for Large Linear Systems, vol. 13 of Cam- bridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, 2003.
(M. E. Hochstenbach) Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB, The Netherlands, www.win.tue.nl/∼hochsten/
E-mail address: m.e.hochstenbach@tue.nl
(D. A. Singer) Department of Mathematics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106-7058, USA.
E-mail address: david.singer@case.edu
(P. F. Zachlin) Department of Mathematics, Lakeland Community College, 7700 Clocktower Drive, Kirtland, OH 44094-5198, USA.
E-mail address: pzachlin@lakelandcc.edu