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Numerical Solution of Algebraic Riccati Equations [Pehme köide]

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  • Formaat: Paperback, 266 pages, kõrgus x laius x paksus: 229x152x14 mm, kaal: 470 g, Illustrations (some col.)
  • Sari: Fundamentals of Algorithms 9
  • Ilmumisaeg: 30-Jan-2012
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611972086
  • ISBN-13: 9781611972085
Teised raamatud teemal:
Numerical Solution of Algebraic Riccati EquationsSuurem pilt
  • Formaat: Paperback, 266 pages, kõrgus x laius x paksus: 229x152x14 mm, kaal: 470 g, Illustrations (some col.)
  • Sari: Fundamentals of Algorithms 9
  • Ilmumisaeg: 30-Jan-2012
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611972086
  • ISBN-13: 9781611972085
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781611972085.html
Märksõnad:
This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way. Some proofs of theoretical results have been simplified and a unified notation has been adopted. Readers will find a discussion of doubling algorithms, which are effective in solving algebraic Riccati equations, and a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations, along with their MATLAB(R) codes. This will help the reader gain understanding of the computational issues and provide ready-to-use implementation of the different solution techniques.
Preface ix
Listings xiii
Notation and Acronyms xv
1 Introduction and preliminaries 1(32)
1.1 Matrix equations
2(1)
1.2 Algebraic Riccati equations
3(5)
1.2.1 Nonsymmetric equations
3(1)
1.2.2 Equations associated with M-matrices
3(2)
1.2.3 Continuous-time equations
5(1)
1.2.4 Discrete-time equations
6(2)
1.3 Unilateral quadratic matrix equations
8(1)
1.4 Useful concepts and definitions
9(13)
1.4.1 Invariant and deflating subspaces
9(2)
1.4.2 Some definitions from control theory
11(1)
1.4.3 Matrix polynomials
12(2)
1.4.4 Eigenvalue transformations
14(6)
1.4.5 Splitting properties
20(2)
1.5 Hamiltonian and symplectic matrices
22(4)
1.6 Algorithmic issues
26(4)
1.6.1 Convergence speed
26(2)
1.6.2 Cost of elementary matrix operations
28(1)
1.6.3 Conditioning and numerical stability
29(1)
1.7 Available software
30(1)
1.8 Additional notes and further reading
31(2)
2 Theoretical analysis 33(50)
2.1 Invariant subspaces and algebraic Riccati equations
33(8)
2.1.1 Nonsymmetric equations
33(4)
2.1.2 Equations associated with M-matrices
37(2)
2.1.3 Continuous-time equations
39(1)
2.1.4 Discrete-time equations
40(1)
2.2 Extremal solutions
41(9)
2.2.1 Equations associated with M-matrices
42(4)
2.2.2 Continuous-time equations
46(3)
2.2.3 Discrete-time equations
49(1)
2.3 Critical solutions
50(2)
2.4 Shift techniques
52(9)
2.4.1 Equations associated with M-matrices
54(3)
2.4.2 Continuous-time equations
57(4)
2.5 Transformations between discrete- and continuous-time
61(1)
2.6 Unilateral quadratic matrix equations
62(5)
2.7 Transforming an algebraic Riccati equation to a UQME
67(8)
2.7.1 Simple transformation
68(2)
2.7.2 UL-based transformation
70(3)
2.7.3 Reduction to a UQME of lower size
73(2)
2.8 Perturbation results
75(6)
2.8.1 Algebraic Riccati equations
76(4)
2.8.2 UQMEs
80(1)
2.9 Additional notes and further reading
81(2)
3 Classical algorithms 83(38)
3.1 Linear matrix equations
83(4)
3.1.1 Sylvester, Lyapunov, and Stein equations
83(4)
3.1.2 Generalized equations
87(1)
3.2 Invariant subspaces methods
87(5)
3.2.1 Balancing technique
92(1)
3.3 Newton's method
92(11)
3.3.1 Continuous-time equations
93(5)
3.3.2 Equations associated with M-matrices
98(3)
3.3.3 Other algebraic Riccati equations
101(1)
3.3.4 Iterative refinement and defect correction
102(1)
3.4 Functional iterations
103(2)
3.5 Matrix sign function method
105(6)
3.5.1 Continuous-time equations
105(2)
3.5.2 Computing the matrix sign function
107(2)
3.5.3 Other algebraic Riccati equations
109(2)
3.6 Numerical experiments
111(7)
3.6.1 Continuous-time equations
111(3)
3.6.2 Equations associated with M-matrices
114(4)
3.7 Additional notes and further reading
118(3)
4 Structured invariant subspace methods 121(24)
4.1 Elementary matrices
122(3)
4.2 Hamiltonian condensed and special forms
125(6)
4.2.1 The PVL form
126(2)
4.2.2 URV Decomposition
128(3)
4.2.3 Other condensed forms
131(1)
4.3 Hamiltonian QR algorithm
131(4)
4.3.1 The Hamiltonian/symplectic QR step
133(2)
4.4 Computation of the eigenvalues of a Hamiltonian matrix
135(1)
4.5 The URV algorithms
136(4)
4.6 The multishift algorithm
140(2)
4.7 Additional notes and further reading
142(3)
5 Doubling algorithms 145(50)
5.1 Structured doubling algorithm
146(9)
5.1.1 SDA-I
147(4)
5.1.2 SDA-II
151(2)
5.1.3 QR-based doubling algorithm
153(2)
5.2 Cyclic reduction
155(13)
5.2.1 Convergence properties
158(3)
5.2.2 Applicability
161(6)
5.2.3 Interplay with SDAs
167(1)
5.3 Solving algebraic Riccati equations
168(20)
5.3.1 Equations associated with M-matrices
168(11)
5.3.2 Continuous-time equations
179(5)
5.3.3 Discrete-time equations
184(4)
5.4 Acceleration techniques
188(2)
5.5 Numerical experiments
190(2)
5.5.1 Continuous-time equations
190(1)
5.5.2 Equations associated with M-matrices
191(1)
5.6 Additional notes and further reading
192(3)
6 Algorithms for large-scale problems 195(14)
6.1 Linear matrix equations with large and sparse coefficients
196(8)
6.1.1 The ADI iteration
196(2)
6.1.2 Cholesky factor ADI
198(3)
6.1.3 Krylov subspace methods
201(3)
6.2 Continuous- and discrete-time Riccati equations
204(2)
6.3 Additional notes and further reading
206(3)
A Basic properties 209(12)
A.1 Norms and spectral radius
209(2)
A.2 Matrix factorizations and decompositions
211(2)
A.3 Krylov subspaces
213(1)
A.4 Properties of Kronecker product
214(1)
A.5 Nonnegative matrices and M-matrices
215(1)
A.6 Matrix functions and Laurent power series
216(1)
A.7 Frechet derivative and its properties
217(1)
A.8 Elementary matrices
218(3)
Bibliography 221(24)
Index 245
Dario A. Bini is Professor of Numerical Analysis at the University of Pisa. He is coauthor of two other books on polynomial and matrix computations and on the numerical solution of Markov chains. He specialises in numerical linear algebra and polynomial computations. Bruno Iannazzo is Researcher in Numerical Analysis at the University of Perugia. His main interests are in the field of numerical linear algebra with specific attention to matrix functions and matrix equations. Beatrice Meini is Associate Professor at the University of Pisa. She is coauthor of a book on the numerical solution of structured Markov chains. Her interests are addressed to numerical linear algebra and its applications with special focus on matrix equations and Markov chains.