rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Methods of intermediate problems for eigenvalues: theory and ramifications
  name:
    name part: Weinstein, Alexander
    name part: 1897-1979
    role:
      role term: creator
  name:
    name part: Stenger, William
    role:
      role term: author.
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    place:
      place term: New York
    publisher: Academic Press
    date issued: 1972
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xi, 236 pages)
  abstract: 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.
  table of contents: 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.
  table of contents: 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.
  table of contents: 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.
  table of contents: 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.
  table of contents: 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.
  note: [by] Alexander Weinstein and William Stenger.
  note: 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. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references (pages 221-231).
  note: English.
  subject:
    topic: Calculus of variations
  subject:
    topic: Eigenvalues
  subject:
    topic: Calcul des variations
  subject:
    topic: Eigenvaleurs
  subject:
    topic: Valeurs propres
  subject:
    topic: MATHEMATICS
    topic: Calculus
  subject:
    topic: MATHEMATICS
    topic: Mathematical Analysis
  subject:
    topic: Calculus of variations
  subject:
    topic: Eigenvalues
  subject:
    topic: Eigenwert
  subject:
    topic: Eigenvalues
  subject:
    topic: Calculus of variations
  subject:
    topic: Calcul des variations
  subject:
    topic: Valeurs propres
  subject:
    topic: Calculus of variations
  subject:
    topic: Eigenvalues
  classification: QA316 .W45
  classification: 515/.64
  classification: SK 520
  classification: SK 620
  classification: SK 660
  related item:
    title info:
      title: Methods of intermediate problems for eigenvalues: theory and ramifications
    name:
      name part: Weinstein, Alexander, 1897-
    origin info:
      publisher: New York, Academic Press, 1972
    identifier: (DLC) 70154367
    identifier: (OCoLC)343604
  related item:
    identifier: (DLC) 70154367
    identifier: (OCoLC)343604
  related item:
    title info:
      title: Mathematics in science and engineering ; v. 89
  identifier: 9780080955988
  identifier: 0080955983
  identifier: 1282702882
  identifier: 9781282702882
  identifier: 9786612702884
  identifier: 6612702885
  identifier: 0127424504
  identifier: 9780127424507
  identifier: 70154367
  identifier: 1093197:10877871 Elsevier Science & Technology
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCLCE
    record creation date: 090107
    record change date: 20260326155928.0
    record identifier: in00005735604
    language of cataloging:
      language term: eng