This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. The estimate is a polynomial ......
This republication addresses some of the basic questions in numerical analysis: convergence theorems for iterative methods for both linear and nonlinear equations; discretization error, especially for ordinary differential equations; rounding error analysis; sensitivity of eigenvalues; and solutions of linear equations with respect to changes in ......
A reprint of the original volume, which won the Lanchester Prize awarded by the Operations Research Society of America for the best work of 1968. Although out of print for nearly 15 years, it remains one of the most referenced volumes in the field of mathematical programming. Recent interest in interior point methods generated by Karmarkar's ......
Mathematical Reviews said of this book that it was ""destined to become a classical reference"". It has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated ......
A need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator splitting methods such as alternating methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics. ......
A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of ......
The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description of this method, which finds invariants of geometric objects under infinite dimensional pseudo-groups, is presented for the first time. As part of the ......
Presents the elements of a unified approach to optimization based on ""nonsmooth analysis,"" a term introduced in the 1970s by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self contained and accessible manner. The topics treated ......
Here is a monograph that describes current research efforts in the application of symbolic computation to several areas, including dynamical systems, differential geometry, Lie algebra's, numerical analysis, fluid dynamics, perturbation theory, control theory, and mechanics. The chapters, which illustrate how symbolic computations can be used to ......
