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Eigenvalues of Matrices 2nd Revised edition [Pehme köide]

  • Formaat: Paperback, 440 pages, kõrgus x laius x paksus: 229x152x22 mm, kaal: 580 g, Illustrations (black and white)
  • Sari: Classics in Applied Mathematics 71
  • Ilmumisaeg: 30-Nov-2012
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611972450
  • ISBN-13: 9781611972450
Teised raamatud teemal:
Eigenvalues of Matrices 2nd Revised editionSuurem pilt
  • Formaat: Paperback, 440 pages, kõrgus x laius x paksus: 229x152x22 mm, kaal: 580 g, Illustrations (black and white)
  • Sari: Classics in Applied Mathematics 71
  • Ilmumisaeg: 30-Nov-2012
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611972450
  • ISBN-13: 9781611972450
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781611972450.html
Märksõnad:
This classic textbook provides a modern and complete guide to the calculation of eigenvalues of matrices, written at an accessible level that presents in matrix notation the fundamental aspects of the spectral theory of linear operators in finite dimension. Unique features of this book are:* The convergence of eigensolvers serving as the basis of the notion of the gap between invariant subspaces.* Its coverage of the impact of the high nonnormality of the matrix on its eigenvalues.* The comprehensive nature of the material that moves beyond mathematical technicalities to the essential mean carried out by matrix eigenvalues.
Preface to the Classics Edition xiii
Preface xv
Preface to the English Edition xix
Notation xxi
List of Errata
xxiii
Chapter 1 Supplements from Linear Algebra
1(60)
1.1 Notation and definitions
1(4)
1.2 The canonical angles between two subspaces
5(3)
1.3 Projections
8(2)
1.4 The gap between two subspaces
10(4)
1.5 Convergence of a sequence of subspaces
14(4)
1.6 Reduction of square matrices
18(9)
1.7 Spectral decomposition
27(4)
1.8 Rank and linear independence
31(1)
1.9 Hermitian and normal matrices
32(1)
1.10 Non-negative matrices
33(1)
1.11 Sections and Rayleigh quotients
34(1)
1.12 Sylvester's equation
35(7)
1.13 Regular pencils of matrices
42(1)
1.14 Bibliographical comments
43(18)
Exercises
43(18)
Chapter 2 Elements of Spectral Theory
61(50)
2.1 Revision of some properties of functions of a complex variable
61(2)
2.2 Singularities of the resolvent
63(10)
2.3 The reduced resolvent and the partial inverse
73(3)
2.4 The block-reduced resolvent
76(3)
2.5 Linear perturbations of the matrix A
79(3)
2.6 Analyticity of the resolvent
82(2)
2.7 Analyticity of the spectral projection
84(1)
2.8 The Rellich-Kato expansions
85(1)
2.9 The Rayleigh-Schrodinger expansions
86(3)
2.10 Non-linear equation and Newton's method
89(3)
2.11 Modified methods
92(3)
2.12 The local approximate inverse and the method of residual correction
95(3)
2.13 Bibliographical comments
98(13)
Exercises
98(13)
Chapter 3 Why Compute Eigenvalues?
111(38)
3.1 Differential equations and difference equations
111(3)
3.2 Markov chains
114(3)
3.3 Theory of economics
117(2)
3.4 Factorial analysis of data
119(1)
3.5 The dynamics of structures
120(2)
3.6 Chemistry
122(2)
3.7 Fredholm's integral equation
124(2)
3.8 Bibliographical comments
126(23)
Exercises
126(23)
Chapter 4 Error Analysis
149(56)
4.1 Revision of the conditioning of a system
149(1)
4.2 Stability of a spectral problem
150(15)
4.3 A priori analysis of errors
165(5)
4.4 A posteriori analysis of errors
170(7)
4.5 A is almost diagonal
177(3)
4.6 A is Hermitian
180(10)
4.7 Bibliographical comments
190(15)
Exercises
191(14)
Chapter 5 Foundations of Methods for Computing Eigenvalues
205(46)
5.1 Convergence of a Krylov sequence of subspaces
205(3)
5.2 The method of subspace iteration
208(5)
5.3 The power method
213(4)
5.4 The method of inverse iteration
217(4)
5.5 The QR algorithm
221(5)
5.6 Hermitian matrices
226(1)
5.7 The QZ algorithm
226(1)
5.8 Newton's method and the Rayleigh quotient iteration
227(1)
5.9 Modified Newton's method and simultaneous inverse iterations
228(7)
5.10 Bibliographical comments
235(16)
Exercises
235(16)
Chapter 6 Numerical Methods for Large Matrices
251(42)
6.1 The principle of the methods
251(2)
6.2 The method of subspace iteration revisited
253(4)
6.3 The Lanczos method
257(9)
6.4 The block Lanczos method
266(4)
6.5 The generalized problem Kx ≠ λMx
270(2)
6.6 Arnoldi's method
272(7)
6.7 Oblique projections
279(1)
6.8 Bibliographical comments
280(13)
Exercises
281(12)
Chapter 7 Chebyshev's Iterative Methods
293(30)
7.1 Elements of the theory of uniform approximation for a compact set in
293(6)
7.2 Chebyshev polynomials of a real variable
299(1)
7.3 Chebyshev polynomials of a complex variable
300(4)
7.4 The Chebyshev acceleration for the power method
304(1)
7.5 The Chebyshev iteration method
305(3)
7.6 Simultaneous Chebyshev iterations (with projection)
308(3)
7.7 Determination of the optimal parameters
311(1)
7.8 Least squares polynomials on a polygon
312(2)
7.9 The hybrid methods of Saad
314(2)
7.10 Bibliographical comments
316(7)
Exercises
316(7)
Chapter 8 Polymorphic Information Processing with Matrices
323(28)
8.1 Scalars in a field
324(1)
8.2 Scalars in a ring
324(3)
8.3 Square matrices are macro-scalars
327(1)
8.4 The spectral and metric information stemming from A of order n
328(2)
8.5 Polar representations of A of order n
330(2)
8.6 The yield of A Hermitian positive semi-definite under spectral coupling
332(8)
8.7 Homotopic deviation
340(2)
8.8 Non-commutativity of the matrix product
342(4)
8.9 Conclusion
346(1)
8.10 Bibliographical comments
346(5)
Exercises
346(2)
Additional References
348(3)
Appendices
351(55)
A Solution to Exercises
351(44)
B References for Exercises
395(4)
C References
399(7)
Index 406
Francoise Chatelin is Professor of Mathematics at the University of Toulouse and head of the Qualitative Computing Group at CERFACS. Before moving to CERFACS, she was a professor at the universities of Grenoble and Paris IX Dauphine. She also worked for a decade in the industrial research laboratories of IBM France and Thales, where she was in charge of intensive computing activities. Her areas of expertise include spectral theory for linear operators in Banach spaces and finite precision computation of very large eigenproblems. She currently explores the uncharted domain of mathematical computation that lies beyond real or complex analysis.