Numerical analysis

Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers.

In the last three decades, advances in methods for investigating polynomial ideals and their varieties have provided new possibilities for approaching two long-standing problems in the theory of differential equations: the Poincare center problem and the cyclicity problem (the problem of bifurcation of limit cycles from singular trajectories).

This monograph, derived from an advanced computer science course at Stanford University, builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions.

The primary focus of this book is on explicating the direct method approach.

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena.

The theory of dynamic games continues to evolve, and one purpose of this volume is to report a number of recent theoretical advances in the ?

Satellite navigation receivers are used to receive, process, and decode space-based navigation signals, such as those provided by the GPS constellation of satellites.

The paradigms of dynamic games play an important role in the development of multi-agent models in engineering, economics, and management science.

The problem of asymptotic regulation of the output of a dynamical system plays a central role in control theory.

The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations.

This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a guide to the vitality and growth of the field.

Prior to the computer era, analytical methods in elasticity had already been developed and - proved up to impressive levels.

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This monograph examines and develops the Global Smoothness Preservation Property (GSPP) and the Shape Preservation Property (SPP) in the field of interpolation of functions.

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This book offers a careful selection of studies in optimization techniques based on artificial intelligence, applied to inverse problems in radiative transfer.

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics.

Contains all state-of-the-art algorithms dealing with multiple-precision integers or floating-point numbers in a ready-to-implement format.

This book presents a short introduction to the main tools of optimization methodology including linear programming, steepest descent, conjugate gradients, and the Karush-Kuhn-Tucker-John conditions.

This text introduces numerical methods and shows how to develop, analyze, and use them.

Can you trust results from modelling and simulation?

Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.

Surveys and summaries of latest research in numerical analysis, optimization, computer algebra and scientific computing.

This text introduces numerical methods and shows how to develop, analyze, and use them.

An interval is a natural way of specifying a number that is specified only within certain tolerances.

Moving frames explained in the language of undergraduate calculus, suitable for graduate students.

First book on the fast multipole BEM, bringing together classical theory in BEM formulations and the fast multipole method.

First book on the fast multipole BEM, bringing together classical theory in BEM formulations and the fast multipole method.

An extensively updated second edition including new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients.

Presents the major mathematical tools necessary for the study of complex dynamics.

This edition of this successful text includes chapters on hyperelastic plastic behaviour and updates to FLagSHyP web program.

A reference/advanced text on part of applied analysis with applications in numerical analysis and computer-aided geometric design.

This thoroughly revised 2007 third edition updates the definitive introduction to finite element methods.

An introduction for graduate students, a guide for users, and a comprehensive resource for experts.

A self-contained introduction to the theory of scattered data approximation, suitable for graduates and researchers.

A 2007 graduate text on spectral methods with applications in fluid dynamics and engineering.

In this introductory text, the fundamental algorithms of numerical linear algebra are developed in a parallel context.

A manual and guide to good scientific computing style, explaining how to write good software and how to test it for bugs, accuracy and performance.

This book, first published in 2004, explores data envelopment analysis, which measures firms'' input-output efficiencies using mathematical programming techniques.

A broad scope textbook for senior undergraduates starting computational physics courses, first published in 2006.

A comprehensive introduction to preconditioning techniques, now an essential part of successful and efficient iterative solutions of matrices.

Gives a complete introduction to partial differential equations and numerical analysis for upper undergraduates and beginning graduates.

A complete theoretical framework and guide to numerical geometric integration techniques.

This book, first published in 2003, provides a concise but sound treatment of ODEs, including IVPs, BVPs, and DDEs.

An introduction to numerical analysis combining rigour with practical applications, and providing numerous exercises plus solutions.

This monograph presents the GRP algorithm and is accessible to researchers and graduate students alike.

This book is concerned with the coherent treatment, including the derivation, analysis, and applications, of the most useful scalar extrapolation methods.

Overview of iterative solutions methods for systems of linear equations.

This book covers the development of high-order numerical methods for the simulation of incompressible fluid flows in complex domains.

A comprehensive bibliography rounds off what will prove a very valuable work.