Variational Methods for Eigenvalue Approximation (CBMS-NSF Regional Conference Series in Applied Mathematics)

✍ Scribed by Hans F. Weinberger

• Publisher: Society for Industrial Mathematics
• Year: 1987
• Tongue: English
• Leaves: 169
• Series: CBMS-NSF Regional Conference Series in Applied Mathematics
• Edition: 2
• Category: Library

✦ Synopsis

Provides a common setting for various methods of bounding the eigenvalues of a self-adjoint linear operator and emphasizes their relationships. A mapping principle is presented to connect many of the methods. The eigenvalue problems studied are linear, and linearization is shown to give important information about nonlinear problems. Linear vector spaces and their properties are used to uniformly describe the eigenvalue problems presented that involve matrices, ordinary or partial differential operators, and integro-differential operators.

✦ Table of Contents

Variational Methods for Eigenvalue Approximation......Page 1
Contents......Page 5
Foreword......Page 7
CHAPTER 1 Prologue: Why Study Eigenvalues ?......Page 9
CHAPTER 2 The Setting: Linear Vector Spaces and Their Properties......Page 27
CHAPTER 3 The Existence and Characterization of Eigenvalues......Page 39
CHAPTER 4 Improvable Bounds for Eigenvalues......Page 75
CHAPTER 5 Eigenvector Approximation......Page 131
CHAPTER 6 Finite Difference Equations......Page 135
CHAPTER 7 Some Other Bounds......Page 149
References......Page 159
INDEX......Page 165