Spectra and Pseudospectra

Name: Spectra and Pseudospectra | The Behavior of Nonnormal Matrices and Operators
Brand: Princeton University Press
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The Behavior of Nonnormal Matrices and Operators

Lloyd N. Trefethen Mark Embree(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 5. Mai 2020

624 Seiten

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978-0-691-21310-1 (ISBN)

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Inhalt

Cover Page
Half-title Page
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgments
I. Introduction
1. Eigenvalues
2. Pseudospectra of matrices
3. A matrix example
4. Pseudospectra of linear operators
5. An operator example
6. History of pseudospectra
II. Toeplitz Matrices
7. Toeplitz matrices and boundary pseudomodes
8. Twisted Toeplitz matrices and wave packet pseudomodes
9. Variations on twisted Toeplitz matrices
III. Differential Operators
10. Differential operators and boundary pseudomodes
11. Variable coefficients and wave packet pseudomodes
12. Advection-diffusion operators
13. Lewy-Hormander nonexistence of solutions
IV. Transient Effects and Nonnormal Dynamics
14. Overview of transients and pseudospectra
15. Exponentials of matrices and operators
16. Powers of matrices and operators
17. Numerical range, abscissa, and radius
18. The Kreiss Matrix Theorem
19. Growth bound theorem for semigroups
V. Fluid Mechanics
20. Stability of fluid flows
21. A model of transition to turbulence
22. Orr-Sommerfeld and Airy operators
23. Further problems in fluid mechanics
VI. Matrix Iterations
24. Gauss-Seidel and SOR iterations
25. Upwind effects and SOR convergence
26. Krylov subspace iterations
27. Hybrid iterations
28. Arnoldi and related eigenvalue iterations
29. The Chebyshev polynomials of a matrix
VII. Numerical Solution of Differential Equations
30. Spectral differentiation matrices
31. Nonmodal instability of PDE discretizations
32. Stability of the method of lines
33. Stiffness of ODEs
34. GKS-stability of boundary conditions
VIII. Random Matrices
35. Random dense matrices
36. Hatano-Nelson matrices and localization
37. Random Fibonacci matrices
38. Random triangular matrices
IX. Computation of Pseudospectra
39. Computation of matrix pseudospectra
40. Projection for large-scale matrices
41. Other computational techniques
42. Pseudospectral abscissae and radii
43. Discretization of continuous operators
44. A flow chart of pseudospectra algorithms
X. Further Mathematical Issues
45. Generalized eigenvalue problems
46. Pseudospectra of rectangular matrices
47. Do pseudospectra determine behavior?
48. Scalar measures of nonnormality
49. Distance to singularity and instability
50. Structured pseudospectra
51. Similarity transformations and canonical forms
52. Eigenvalue perturbation theory
53. Backward error analysis
54. Group velocity and pseudospectra
XI. Further Examples and Applications
55. Companion matrices and zeros of polynomials
56. Markov chains and the cutoff phenomenon
57. Card shuffling
58. Population ecology
59. The Papkovich-Fadle operator
60. Lasers
References
Index

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