05430cam a2200601Ki 4500 ocn962753358 OCoLC 20190328114817.0 m o d cr cnu---unuuu 161116s2016 enka ob 001 0 eng d N$T eng rda pn N$T IDEBK EBLCP YDX OPELS OCLCF IDB OCLCQ WTU OTZ CNCGM OCLCQ U3W MERUC D6H OCLCQ EZ9 OCLCQ WYU MERER OCLCQ 962840668 964529140 967028571 967571204 969416542 975020862 975078454 978769254 1066466898 9780081010907 (electronic bk.) 0081010907 (electronic bk.) 1785481436 9781785481437 (OCoLC)962753358 (OCoLC)962840668 (OCoLC)964529140 (OCoLC)967028571 (OCoLC)967571204 (OCoLC)969416542 (OCoLC)975020862 (OCoLC)975078454 (OCoLC)978769254 (OCoLC)1066466898 QA379 .H46 2016eb MAT 005000 bisacsh MAT 034000 bisacsh 515/.35 23 Henry, J. (Jacques), author. Factorization of boundary value problems using the invariant embedding method / [electronic resource] Jacques Henry, Angel M. Ramos. London : ISTE Press Ltd ; Kidlington, Oxford : Elsevier Ltd, 2016 �2016 1 online resource (xvii, 238 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics and statistics Includes bibliographical references (pages 223-236) and index. Print version record. Front Cover ; Dedication ; Factorization of Boundary Value Problems Using the Invariant Embedding Method; Copyright ; Contents; Preface; Chapter 1. Presentation of the Formal Computation of Factorization; 1.1. Definition of the model problem and its functional framework; 1.2. Direct invariant embedding; 1.3. Backward invariant embedding; 1.4. Internal invariant embedding; Chapter 2. Justification of the Factorization Computation; 2.1. Functional framework; 2.2. Semi-discretization; 2.3. Passing to the limit; Chapter 3. Complements to the Model Problem. 3.1. An alternative method for obtaining the factorization3.2. Other boundary conditions; 3.3. Explicitly taking into account the boundary conditions and the right-hand side; 3.4. Periodic boundary conditions in x; 3.5. An alternative but unstable formulation; 3.6. Link with the Steklov-Poincar�e operator; 3.7. Application of the Schwarz kernel theorem: link with Green's functions and Hadamard's formula; Chapter 4. Interpretation of the Factorization through a Control Problem; 4.1. Formulation of problem (P0) in terms of optimal control. 4.2. Summary of results on the decoupling of optimal control problems4.3. Summary of results of A. Bensoussan on Kalman optimal filtering; 4.4. Parabolic regularization for the factorization of elliptic boundary value problems; Chapter 5. Factorization of the Discretized Problem; 5.1. Introduction and problem statement; 5.2. Application of the factorization method to problem (Ph); 5.3. A second method of discretization; 5.4. A third possibility: centered scheme; 5.5. Row permutation; 5.6. Case of a discretization of the section by finite elements; Chapter 6. Other Problems. 6.1. General second-order linear elliptic problems6.2. Systems of coupled boundary value problems; 6.3. Linear elasticity system; 6.4. Problems of order higher than 2; 6.5. Stokes problems; 6.6. Parabolic problems; Chapter 7. Other Shapes of Domain; 7.1. Domain generalization: transformation preserving orthogonal coordinates; 7.2. Quasi-cylindrical domains with normal velocity fields; 7.3. Sweeping the domain by surfaces of arbitrary shape; Chapter 8. Factorization by the QR Method; 8.1. Normal equation for problem (P0) in section 1.1. 8.2. Factorization of the normal equation by invariant embedding8.3. The QR method; Chapter 9. Representation Formulas for Solutions of Riccati Equations; 9.1. Representation formulas; 9.2. Diagonalization of the two-point boundary value problem; 9.3. Homographic representation of P(x); 9.4. Factorization of problem (P0) with a Dirichlet condition at x =0; Appendix. Gaussian LU Factorization as a Method of Invariant Embedding; A.1. Invariant embedding for a linear system; A.2. Block tridiagonal systems; Bibliography; Index; Back Cover. Boundary value problems. Factorization (Mathematics) Invariant imbedding. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Boundary value problems. fast (OCoLC)fst00837122 Factorization (Mathematics) fast (OCoLC)fst00919711 Invariant imbedding. fast (OCoLC)fst00977977 Electronic books. Electronic book. Ramos, Angel M., author. Print version: Henry, J. (Jacques). Factorization of boundary value problems using the invariant embedding method. London : ISTE Press Ltd ; Kidlington, Oxford : Elsevier Ltd, [2016] 1785481436 (OCoLC)945105395 Mathematics and statistics series (ISTE) ScienceDirect http://www.sciencedirect.com/science/book/9781785481437 247463 247463