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Functional Analysis and Approximation Theory in Numerical Analysis

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Surveys the enormous literature on numerical approximation of solutions of elliptic boundary problems by means of variational and finite element methods, requiring almost constant application of results and techniques from functional analysis and approximation theory to the field of numerical analysis.

Author(s): R. S. Varga
Series: CBMS-NSF Regional Conference Series in Applied Mathematics
Edition: SIAM
Publisher: Society for Industrial Mathematics
Year: 1987

Language: English
Pages: 87

Functional Analysis and Approximation Theory in Numerical Analysis......Page 1
Contents......Page 7
Preface......Page 9
CHAPTER 1 L-Splines......Page 11
CHAPTER 2 Generalizations of L-Splines......Page 21
CHAPTER 3 Interpolation and Approximation Results for Piecewise-Polynomials in Higher Dimensions......Page 27
CHAPTER 4 The Rayleigh-Ritz-Galerkin Method for Nonlinear Boundary Value Problems......Page 35
CHAPTER 5 Fourier Analysis......Page 45
CHAPTER 6 Least Squares Methods......Page 53
CHAPTER 7 Eigenvalue Problems......Page 61
CHAPTER 8 Parabolic Problems......Page 69
CHAPTER 9 Chebyshev Semidiscrete Approximations for Linear Parabolic Problems......Page 79