TY  - BOOK
AU  - Börm,Steffen
AU  - Mehl,Christian
TI  - Numerical Methods for Eigenvalue Problems
T2  - De Gruyter Textbook
SN  - 9783110250374
AV  - QA193 .B67 2012 
U1  - 512.9/436512.9436 
PY  - 2012///
CY  - Berlin
PB  - De Gruyter
KW  - Eigenvalues
KW  - Eigenvectors
KW  - Matrices
KW  - Data processing
KW  - Valeurs propres
KW  - Vecteurs
KW  - Informatique
KW  - MATHEMATICS
KW  - Algebra
KW  - Elementary
KW  - bisacsh
KW  - fast
KW  - Numerisches Verfahren
KW  - gnd
KW  - Eigenwertproblem
KW  - Electronic books
N1  - Preface; 1 Introduction; 1.1 Example: Structural mechanics; 1.2 Example: Stochastic processes; 1.3 Example: Systems of linear differential equations; 2 Existence and properties of eigenvalues and eigenvectors; 2.1 Eigenvalues and eigenvectors; 2.2 Characteristic polynomials; 2.3 Similarity transformations; 2.4 Some properties of Hilbert spaces; 2.5 Invariant subspaces; 2.6 Schur decomposition; 2.7 Non-unitary transformations; 3 Jacobi iteration; 3.1 Iterated similarity transformations; 3.2 Two-dimensional Schur decomposition; 3.3 One step of the iteration; 3.4 Error estimates; 3.5 Quadratic convergence4 Power methods; 4.1 Power iteration; 4.2 Rayleigh quotient; 4.3 Residual-based error control; 4.4 Inverse iteration; 4.5 Rayleigh iteration; 4.6 Convergence to invariant subspace; 4.7 Simultaneous iteration; 4.8 Convergence for general matrices; 5 QR iteration; 5.1 Basic QR step; 5.2 Hessenberg form; 5.3 Shifting; 5.4 Deflation; 5.5 Implicit iteration; 5.6 Multiple-shift strategies; 6 Bisection methods; 6.1 Sturm chains; 6.2 Gershgorin discs; 7 Krylov subspace methods for large sparse eigenvalue problems; 7.1 Sparse matrices and projection methods; 7.2 Krylov subspaces7.3 Gram-Schmidt process; 7.4 Arnoldi iteration; 7.5 Symmetric Lanczos algorithm; 7.6 Chebyshev polynomials; 7.7 Convergence of Krylov subspace methods; 8 Generalized and polynomial eigenvalue problems; 8.1 Polynomial eigenvalue problems and linearization; 8.2 Matrix pencils; 8.3 Deflating subspaces and the generalized Schur decomposition; 8.4 Hessenberg-triangular form; 8.5 Deflation; 8.6 The QZ step; Bibliography; Index
N2  - This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behaviour. Several programming examples allow the reader to experience the behaviour of the different algorithms first-hand. The book addresses students and lecturers of mathematics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to solve ne
UR  - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=471055
ER  -