Inverse Eigenvalue problems : theory, algorithms, and applications / Moody T. Chu and Gene H. Golub.

Format:

Book

Author/Creator:

Chu, Moody.

Contributor:

Golub, Gene H. (Gene Howard), 1932-2007.

Series:

Numerical mathematics and scientific computation.

Numerical mathematics and scientific computation

Language:

English

Subjects (All):

Eigenvalues.

Algebra.

Physical Description:

1 online resource (408 p.)

Place of Publication:

Oxford : Oxford University Press, 2005.

Language Note:

English

Summary:

Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear

Contents:

Contents; List of Acronyms; List of Figures; List of Tables; 1 Introduction; 1.1 Direct problem; 1.2 Inverse problem; 1.2.1 Constraints; 1.2.2 Fundamental issues; 1.3 Nomenclature; 1.4 Summary; 2 Applications; 2.1 Overview; 2.2 Pole assignment problem; 2.2.1 State feedback control; 2.2.2 Output feedback control; 2.3 Applied mechanics; 2.3.1 A string with beads; 2.3.2 Quadratic eigenvalue problem; 2.3.3 Engineering applications; 2.4 Inverse Sturm-Liouville problem; 2.5 Applied physics; 2.5.1 Quantum mechanics; 2.5.2 Neuron transport theory; 2.6 Numerical analysis; 2.6.1 Preconditioning

2.6.2 Numerical ODEs2.6.3 Quadrature rules; 2.7 Signal and data processing; 2.7.1 Signal processing; 2.7.2 Computer algebra; 2.7.3 Molecular structure modelling; 2.7.4 Principal component analysis, data mining and others; 2.8 Summary; 3 Parameterized inverse eigenvalue problems; 3.1 Overview; 3.1.1 Generic form; 3.1.2 Variations; 3.2 General results for linear PIEP; 3.2.1 Existence theory; 3.2.2 Sensitivity analysis; 3.2.3 Ideas of computation; 3.2.4 Newton's method (for LiPIEP2); 3.2.5 Projected gradient method (for LiPIEP2); 3.3 Additive inverse eigenvalue problems; 3.3.1 Solvability

3.3.2 Sensitivity and stability (for AIEP2)3.3.3 Numerical methods; 3.4 Multiplicative inverse eigenvalue problems; 3.4.1 Solvability; 3.4.2 Sensitivity (for MIEP2); 3.4.3 Numerical methods; 3.5 Summary; 4 Structured inverse eigenvalue problems; 4.1 Overview; 4.2 Jacobi inverse eigenvalue problems; 4.2.1 Variations; 4.2.2 Physical interpretations; 4.2.3 Existence theory; 4.2.4 Sensitivity issues; 4.2.5 Numerical methods; 4.3 Toeplitz inverse eigenvalue problems; 4.3.1 Symmetry and parity; 4.3.2 Existence; 4.3.3 Numerical methods; 4.4 Nonnegative inverse eigenvalue problems

4.4.1 Some existence results4.4.2 Symmetric nonnegative inverse eigenvalue problem; 4.4.3 Minimum realizable spectral radius; 4.5 Stochastic inverse eigenvalue problems; 4.5.1 Existence; 4.5.2 Numerical method; 4.6 Unitary Hessenberg inverse eigenvalue problems; 4.7 Inverse eigenvalue problems with prescribed entries; 4.7.1 Prescribed entries along the diagonal; 4.7.2 Prescribed entries at arbitrary locations; 4.7.3 Additive inverse eigenvalue problem revisit; 4.7.4 Cardinality and locations; 4.7.5 Numerical methods; 4.8 Inverse singular value problems; 4.8.1 Distinct singular values

5.4 Monic quadratic inverse eigenvalue problem

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

9786611190446

1-281-19044-6

0-19-152422-0

1-4356-2088-7

OCLC:

191091473