Iterative Methods for Linear and Nonlinear Equations
by C.T. Kelley
Publisher: SIAM 1995
Number of pages: 172
This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods.
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by George Benthien
Tutorial discussing some of the numerical aspects of practical harmonic analysis. Topics include Historical Background, Fourier Series and Integral Approximations, Convergence Improvement, Differentiation of Fourier Series and Sigma Factors, etc.
by James M. McDonough - University of Kentucky
These notes cover the following topics: Numerical linear algebra; Solution of nonlinear equations; Approximation theory; Numerical solution of ordinary differential equations; Numerical solution of partial differential equations.
by B. Piette - University of Durham
In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.
by K. Nandakumar - University of Alberta
Contents: On mathematical models; Single nonlinear algebraic equation; System of linear and nonlinear algebraic equations; Numerical differentiation and integration; Ordinary differential equations; Boundary value problems; etc.