Theoretical Numerical Analysis

This book prepares graduate students for research in numerical analysis/computational mathematics by giving a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps them to move rapidly into a research program.

Covers basic results of functional analysis and also some additional topics which are needed in theoretical numerical analysis Exercises at the end of most sections are included (419) Short discussion of the literature, including recommendations for additional reading is provided at the end of each chapter Includes supplementary material: sn.pub/extras

Inhalt
Linear Spaces.- Linear Operators on Normed Spaces.- Approximation Theory.- Fourier Analysis and Wavelets.- Nonlinear Equations and Their Solution by Iteration.- Finite Difference Method.- Sobolev Spaces.- Weak Formulations of Elliptic Boundary Value Problems.- The Galerkin Method and Its Variants.- Finite Element Analysis.- Elliptic Variational Inequalities and Their Numerical Approximations.- Numerical Solution of Fredholm Integral Equations of the Second Kind.- Boundary Integral Equations.- Multivariable Polynomial Approximations.