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Methods of intermediate problems for eigenvalues: theory and ramifications / [by] Alexander Weinstein and William Stenger
Mitwirkende(r): Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Mathematics in science and engineering ; v. 89Verlag: New York : Academic Press, 2010Beschreibung: Online Ressource (xi, 236 pages)ISBN:- 9780127424507
- 9780080955988
- 0080955983
- 0127424504
- 9780127424507
- 515.64
- QA316
Inhalte:
Zusammenfassung: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rankPPN: PPN: 878886710Package identifier: Produktsigel: BSZ-33-EBS-C1UB | BSZ-33-EBS-HSAA | GBV-33-EBS-MRI | GBV-33-EBS-ZHB | GBV-33-Freedom-BL | ZDB-1-ELC | ZDB-33-EBS | ZDB-33-ESD
Front Cover; Methods of Intermediate Problems for Eigenvalues; Copyright Page; Contents; Preface; Acknowledgments; Introduction; CHAPTER ONE The Variational Characterization of Eigenvalues; 1. A Preliminary Survey of the Classical and Minimax Principles for Eigenvalues; 2. Operators of Class S; 3. Rayleigh's Principle and the Classical Characterization; CHAPTER TWO The Rayleigh-Ritz Method; 1. Poincaré's Inequalities: The Theoretical Foundation of the Rayleigh-Rit Method; 2. The Minimum-Maximum Principle; 3. Upper Bounds for Eigenvalues
4. A Necessary and Sufficient Criterion in the Minimum-Maximum Theory5. The Principle of Monotonicity; CHAPTER THREE The Classical Maximum-Minimum Theory and Its Extension to Unbounded Operators; 1. Weyl's First Fundamental Lemma; 2. The Maximum-Minimum Principle; 3. The Existence of Minima for Semibounded Operators; 4. Comparison of the Minimum-Maximum and Maximum-Minimum Principles; 5. Finite-Dimensional Spaces; 6. THe General Maxi-Mini-Max Principle; CHAPTER FOUR Intermediate Problems of The First Type; 1. Weinstein's General Scheme of Intermediate Problems
2. The Basic Principles of Intermediate Problems of the First Type3. Nonpersistent Eigenvalues, Weinstein's Determinant; 4. The Distinguished Choice; 5. Lower Bounds Using a Distingushed Choice; 6. The Existence of Distinguished Choices; 7. The General Choice; 8. Aronszajn's Rule for the Theoretical Determination of Eigenvalues; 9. Comparison of the Various Rules; 10. Weinberger-Bazley-Fox Method of Truncation; 11. Convergence; 12. Computation of Lower Bounds for the Buckling of a Clamped plate; 13. On the Symmetries of the Eigenfunctions; 14. Weyl's Second Lemma
CHAPTER FIVE Intermediate Problems of The Second Type1. Formulation of Problems of the Second Type; 2. Finite Rank Perturbations and Intermediate Problems of the Second Type; 3. A Solution of the Second Type; 4. Bazley's Special Choice; 5. The General Choice and Truncation; 6. The Existence of a Base Problem for a Compact Operator; 7. The Spectrum of the Helium Atom; 8. Application of the Special Choice to the Helium Atom; 9. Application of Intermediate Problems to Temple's Formula; 10. Application of Truncation to Quantum Theory
CHAPTER SIX Various Other Methods and Their Connections with Intermediate Problems1. Quadratic Forms and Intermediate Problems; 2. Application of Quadratic Forms to Free and Cantilever Plates; 3. The Rhombical Membrane; 4. Bazley-Fox Method for Sums of Solvable Operators; 5. The Trefftz-Fichera Method for Integral Operators; 6. Fichera's Construction of Intermediate Green's Operators; CHAPTER SEVEN The New Maximum-Minimum Theory; 1. The Basis of Weinstein's New Maximum-Minimum Theory; 2. The Case of One Constraint; 3. The Case of Orthonormal Constraints; 4. The General Formulation
5. A Special Property of Operators Having Finite Traces
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