Afternotes Goes to Graduate School

by Stewart, G. W.

• ISBN13: 9780898714043
• ISBN10: 0898714044
• Format: Paperback
• Copyright: 1998-05-01
• Publisher: Society for Industrial & Applied

Summary

In this follow-up to Afternotes on Numerical Analysis (SIAM, 1996) the author continues to bring the immediacy of the classroom to the printed page. Like the original undergraduate volume, Afternotes Goes to Graduate School is the result of the author writing down his notes immediately after giving each lecture; in this case the afternotes are the result of a follow-up graduate course taught by Professor Stewart at the University of Maryland. The algorithms presented in this volume require deeper mathematical understanding than those in the undergraduate book, and their implementations are not trivial. Stewart uses a fresh presentation that is clear and intuitive as he covers topics such as discrete and continuous approximation, linear and quadratic splines, eigensystems, and Krylov sequence methods. He concludes with two lectures on classical iterative methods and nonlinear equations.

Table of Contents

Approximation

Lecture

General observations

Decline and fall

The linear sine

Approximation in normed linear spaces

Significant differences

Lecture

The space C[0,1]

Existence of best approximations

Uniqueness of best approximations

Convergence in C[0,1]

The Weierstrass approximation theorem

Bernstein polynomials

Comments

Lecture

Chebyshev approximation

Uniqueness

Convergence of Chebyshev approximations

Rates of convergence

Linear and Cubic Splines

Lecture

Piecewise linear interpolation

The error in L(f)

Approximations in the $ infty$-norm

Hat functions

Integration

Least squares approximation

Implementations issues

Lecture

Cubic splines

Derivation of the cubic spline

End conditions

Convergence

Locality

Eigensystems

Eigensystems

Krylov Sequence Methods

Iterations, Linear and Nonlinear

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