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Methods of intermediate problems for eigenvalues: theory and ramifications
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-Lagrang...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York,
Academic Press,
1972.
|
| Colección: | Mathematics in science and engineering ;
v. 89. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
MARC
| LEADER | 00000cam a2200000 4500 | ||
|---|---|---|---|
| 001 | SCIDIR_ocn297337878 | ||
| 003 | OCoLC | ||
| 005 | 20231117032816.0 | ||
| 006 | m o d | ||
| 007 | cr unu---uuaua | ||
| 008 | 090107s1972 nyu ob 001 0 eng d | ||
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| 020 | |z 9780127424507 | ||
| 035 | |a (OCoLC)297337878 |z (OCoLC)428097275 |z (OCoLC)643528867 |z (OCoLC)649906544 |z (OCoLC)813230951 |z (OCoLC)907156343 |z (OCoLC)987452288 |z (OCoLC)1086435502 |z (OCoLC)1162071288 |z (OCoLC)1280800427 | ||
| 042 | |a dlr | ||
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| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 082 | 0 | 4 | |a 515/.64 |
| 100 | 1 | |a Weinstein, Alexander, |d 1897-1979. | |
| 245 | 1 | 0 | |a Methods of intermediate problems for eigenvalues: theory and ramifications |c [by] Alexander Weinstein and William Stenger. |
| 260 | |a New York, |b Academic Press, |c 1972. | ||
| 300 | |a 1 online resource (xi, 236 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mathematics in science and engineering, |v v. 89 | |
| 504 | |a Includes bibliographical references (pages 221-231). | ||
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2010. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2010 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. Poincar�e's Inequalities: The Theoretical Foundation of the Rayleigh-Rit Method; 2. The Minimum-Maximum Principle; 3. Upper Bounds for Eigenvalues. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a 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-rank. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Calculus of variations. | |
| 650 | 0 | |a Eigenvalues. | |
| 650 | 6 | |a Calcul des variations. |0 (CaQQLa)201-0001183 | |
| 650 | 6 | |a Eigenvaleurs. | |
| 650 | 6 | |a Valeurs propres. |0 (CaQQLa)201-0069892 | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Calculus of variations |2 fast |0 (OCoLC)fst00844140 | |
| 650 | 7 | |a Eigenvalues |2 fast |0 (OCoLC)fst00904031 | |
| 650 | 7 | |a Eigenwert |2 gnd |0 (DE-588)4151200-5 | |
| 700 | 1 | |a Stenger, William, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Weinstein, Alexander, 1897- |t Methods of intermediate problems for eigenvalues: theory and ramifications. |d New York, Academic Press, 1972 |z 0127424504 |z 9780127424507 |w (DLC) 70154367 |w (OCoLC)343604 |
| 830 | 0 | |a Mathematics in science and engineering ; |v v. 89. | |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780127424507 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/bookseries/00765392/89 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/publication?issn=00765392&volume=89 |z Texto completo |