Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Lloyd N. Trefethen and Mark Embree
Title: Spectra and pseudospectra: The behavior of nonnormal matrices and operators
Additional book information: Princeton Univ. Press, Princeton, NJ, 2005, xvii + 606 pp., ISBN 0-691-11946-5, US$65.00

References [Enhancements On Off] (What's this?)

  • 1. Zhaojun Bai and James W. Demmel, On a block implementation of Hessenberg multishift QR iteration, Int. J. High Speed Computing 1 (1989), no. 1, 97-112.
  • 2. R. E. D. Bishop, Arthur Roderick Collar. 22 February 1908-12 February 1986, Biographical Memoirs of Fellows of the Royal Society 33 (1987), 164-185.
  • 3. Albrecht Böttcher and Sergei M. Grudsky, Spectral properties of banded Toeplitz matrices, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005. MR 2179973
  • 4. Karen Braman, Ralph Byers, and Roy Mathias, The multishift 𝑄𝑅 algorithm. I. Maintaining well-focused shifts and level 3 performance, SIAM J. Matrix Anal. Appl. 23 (2002), no. 4, 929–947. MR 1920926,
  • 5. E. B. Davies, Pseudo-spectra, the harmonic oscillator and complex resonances, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 455 (1999), no. 1982, 585–599. MR 1700903,
  • 6. E. B. Davies and Barry Simon, Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle, J. Approx. Theory 141 (2006), no. 2, 189-213.
  • 7. Nils Dencker, Johannes Sjöstrand, and Maciej Zworski, Pseudospectra of semiclassical (pseudo-) differential operators, Comm. Pure Appl. Math. 57 (2004), no. 3, 384–415. MR 2020109,
  • 8. Jack J. Dongarra and Francis Sullivan, Introduction to the top 10 algorithms, Computing in Science and Engineering 2 (2000), no. 1, 22-23.
  • 9. C. A. Felippa, A historical outline of matrix structural analysis: A play in three acts, Computers and Structures 79 (2001), 1313-1324.
  • 10. R. A. Frazer, W. J. Duncan, and A. R. Collar, Elementary Matrices and Some Applications to Dynamics and Differential Equations, Cambridge, at the University Press; New York, the Macmillan Company, 1946. MR 0019077
  • 11. S. J. Hammarling and J. H. Wilkinson, The practical behaviour of linear iterative methods with particular reference to S.O.R., Report NAC 69, National Physical Laboratory, Teddington, UK, September 1976.
  • 12. Nicholas J. Higham, An interview with Peter Lancaster, SIAM News 38 (2005), no. 6, 5-6.
  • 13. Nicholas J. Higham, D. Steven Mackey, Niloufer Mackey, and Françoise Tisseur, Symmetric linearizations for matrix polynomials, MIMS EPrint 2005.25, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, November 2005; to appear in SIAM J. Matrix Anal. Appl.
  • 14. Nicholas J. Higham and Françoise Tisseur, More on pseudospectra for polynomial eigenvalue problems and applications in control theory, Linear Algebra Appl. 351/352 (2002), 435–453. Fourth special issue on linear systems and control. MR 1917486,
  • 15. Ilse C. F. Ipsen, Accurate eigenvalues for fast trains, SIAM News 37 (2004), no. 9, 1-2.
  • 16. Modern computing methods, Notes on applied science, no. 16, National Physical Laboratory, Teddington, England. Her Majesty’s Stationery Office, London, 1957. MR 0088783
  • 17. Peter Lancaster, Lambda-matrices and vibrating systems, International Series of Monographs in Pure and Applied Mathematics, Vol. 94, Pergamon Press, Oxford-New York-Paris, 1966. MR 0210345
    Peter Lancaster, Lambda-matrices and vibrating systems, Dover Publications, Inc., Mineola, NY, 2002. Reprint of the 1966 original [Pergamon Press, New York; MR0210345 (35 #1238)]. MR 1949393
  • 18. Amy N. Langville and Carl D. Meyer, Google's PageRank and beyond: The science of search engine rankings, Princeton University Press, Princeton, NJ, USA, 2006.
  • 19. D. Steven Mackey, Niloufer Mackey, Christian Mehl, and Volker Mehrmann, Vector spaces of linearizations for matrix polynomials, Numerical Analysis Report No. 464, Manchester Centre for Computational Mathematics, Manchester, England, April 2005; to appear in SIAM J. Matrix Anal. Appl.
  • 20. -, Structured polynomial eigenvalue problems: Good vibrations from good linearizations, MIMS EPrint 2006.38, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, March 2006; to appear in SIAM J. Matrix Anal. Appl.
  • 21. Volker Mehrmann and Heinrich Voss, Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods, GAMM Mitt. Ges. Angew. Math. Mech. 27 (2004), no. 2, 121–152 (2005). MR 2124762,
  • 22. Cleve B. Moler, Cleve's Corner: The world's largest matrix computation: Google's PageRank is an eigenvector of a matrix of order 2.7 billion, MATLAB News and Notes (October 2002).
  • 23. Beresford N. Parlett, The QR algorithm, Computing in Science and Engineering 2 (2000), no. 1, 38-42.
  • 24. Hans Schneider, Olga Taussky-Todd’s influence on matrix theory and matrix theorists, Linear and Multilinear Algebra 5 (1977/78), no. 3, 197–224. A discursive personal tribute. MR 460043,
  • 25. Olga Taussky, How I became a torchbearer for matrix theory, Amer. Math. Monthly 95 (1988), no. 9, 801–812. MR 967341,
  • 26. Françoise Tisseur and Karl Meerbergen, The quadratic eigenvalue problem, SIAM Rev. 43 (2001), no. 2, 235–286. MR 1861082,
  • 27. J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
  • 28. James H. Wilkinson, The perfidious polynomial, Studies in numerical analysis, MAA Stud. Math., vol. 24, Math. Assoc. America, Washington, DC, 1984, pp. 1–28. MR 925210
  • 29. Thomas George Wright, Algorithm and software for pseudospectra, Ph.D. thesis, Numerical Analysis Group, Oxford University Computing Laboratory, Oxford, UK, 2002, pp. vi+150.
  • 30. Maciej Zworski, A remark on a paper of E. B Davies: “Semi-classical states for non-self-adjoint Schrödinger operators” [Comm. Math. Phys. 200 (1999), no. 1, 35–41; MR1671904 (99m:34197)], Proc. Amer. Math. Soc. 129 (2001), no. 10, 2955–2957. MR 1840099,
  • 31. Maciej Zworski, Numerical linear algebra and solvability of partial differential equations, Comm. Math. Phys. 229 (2002), no. 2, 293–307. MR 1923176,

Review Information:

Reviewer: Nicholas J. Higham
Affiliation: The University of Manchester
Journal: Bull. Amer. Math. Soc. 44 (2007), 277-284
MSC (2000): Primary 65F15; Secondary 15A18
Published electronically: October 20, 2006
Review copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.