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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$65.00$
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.
Albrecht Böttcher and Sergei M. Grudsky, Spectral properties of banded Toeplitz matrices, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005. MR 2179973, DOI 10.1137/1.9780898717853
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, DOI 10.1137/S0895479801384573
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, DOI 10.1098/rspa.1999.0325
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.
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, DOI 10.1002/cpa.20004
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.
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; The Macmillan Company, New York, 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.
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, DOI 10.1016/S0024-3795(01)00542-0
15. Ilse C. F. Ipsen, Accurate eigenvalues for fast trains, SIAM News 37 (2004), no. 9, 1-2.
Modern computing methods, National Physical Laboratory, Teddington, England; Her Majesty’s Stationery Office, London, 1957. Notes on applied science, no. 16. MR 0088783
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
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.
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, DOI 10.1002/gamm.201490007
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.
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, DOI 10.1080/03081087708817197
Olga Taussky, How I became a torchbearer for matrix theory, Amer. Math. Monthly 95 (1988), no. 9, 801–812. MR 967341, DOI 10.2307/2322895
Françoise Tisseur and Karl Meerbergen, The quadratic eigenvalue problem, SIAM Rev. 43 (2001), no. 2, 235–286. MR 1861082, DOI 10.1137/S0036144500381988
J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
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.
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, DOI 10.1090/S0002-9939-01-05909-3
Maciej Zworski, Numerical linear algebra and solvability of partial differential equations, Comm. Math. Phys. 229 (2002), no. 2, 293–307. MR 1923176, DOI 10.1007/s00220-002-0683-6
- 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, Philadelphia, PA, USA, 2005. MR 2179973
- 4.
- Karen Braman, Ralph Byers, and Roy Mathias, The multishift QR algorithm. Part I: Maintaining well-focused shifts and level
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, Proc. R. Soc. Lond. A. 455 (1999), no. 1, 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 University Press, 1938, 1963 printing. 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. MR 1917486
- 15.
- Ilse C. F. Ipsen, Accurate eigenvalues for fast trains, SIAM News 37 (2004), no. 9, 1-2.
- 16.
- National Physical Laboratory, Modern computing methods, Notes on Applied Science, no. 16, Her Majesty's Stationery Office, London, 1957. MR 0088783
- 17.
- Peter Lancaster, Lambda-matrices and vibrating systems, Pergamon Press, Oxford, 1966; reprinted by Dover, New York, 2002. MR 0210345, 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-Mitteilungen (GAMM-Reports) 27 (2004), 121-152. 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: A discursive personal tribute, Linear and Multilinear Algebra 5 (1977), 197-224. MR 0460043
- 25.
- Olga Taussky, How I became a torchbearer for matrix theory, Amer. Math. Monthly 95 (1988), no. 9, 801-812. MR 0967341
- 26.
- Françoise Tisseur and Karl Meerbergen, The quadratic eigenvalue problem, SIAM Rev. 43 (2001), no. 2, 235-286. MR 1861082
- 27.
- James H. Wilkinson, Rounding errors in algebraic processes, Notes on Applied Science No. 32, Her Majesty's Stationery Office, London, 1963. Also published by Prentice-Hall, Englewood Cliffs, NJ, USA; reprinted by Dover, New York, 1994. MR 0161456
- 28.
- James H. Wilkinson, The perfidious polynomial, Studies in Numerical Analysis (G. H. Golub, ed.), Studies in Mathematics, vol. 24, Mathematical Association of America, Washington, D.C., 1984, pp. 1-28. MR 0925210
- 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, Proc. Amer. Math. Soc. 129 (2001), no. 10, 2955-2957. MR 1840099
- 31.
- -, Numerical linear algebra and solvability of partial differential equations, Commun. Math. Phys. 229 (2002), no. 2, 293-307. MR 1923176
Review Information:
Reviewer:
Nicholas J. Higham
Affiliation:
The University of Manchester
Email:
higham@ma.man.ac.uk
Journal:
Bull. Amer. Math. Soc.
44 (2007), 277-284
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.
