Cuyt A., Wuytack L. Studies in Computational Mathematics. Volume 1: Nonlinear Methods in Numerical Analysis

North-Holland, 1987. — 282 p.
Most textbooks on Numerical Analysis discuss linear techniques for the solution o various numerical problems. 01ily a small number of books introduce and illustrate nonlinear methods.
This book accumulates several nonlinear techniques mainly resulting from the use of Pade approximants and rational interpolants. First these types of rational approximants are introducrd and afterwards methods based on their use are developed for the solution of standard problems in numerical mathematics: convergence acceleration, initial value problems, boundary value problems, quadrature, nonlinear equations, partial differential equations and integral equations. The problems are allowed to be univariate or multivariate.