Numerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science Based on a successful course at Oxford University, this book covers a wide range of such problems ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations Throughout the book, particular attention is paid to the essential qualities of a numerical algorithm - stability, accuracy, reliability and efficiency The authors go further than simply providing recipes for solving computational problems They carefully analyse the reasons why methods might fail to give accurate answers, or why one method might return an answer in seconds while another would take billions of years This book is ideal as a text for students in the second year of a university mathematics course It combines practicality regarding applications with consistently high standards of rigour

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The numerical treatment of a single nonlinear equation

An introduction to numerical analysis

Many mechanics and physics problems have variational formulations making them appropriate for numerical treatment by finite element techniques and efficient iterative methods. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids. Finite element approximations and non-linear relaxation, augmented Lagrangians, and nonlinear least square methods are all covered in detail, as are many applications. "Numerical Methods for Nonlinear Variational Problems," originally published in the Springer Series in Computational Physics, is a classic in applied mathematics and computational physics and engineering. This long-awaited softcover re-edition is still a valuable resource for practitioners in industry and physics and for advanced students.

Lectures on Numerical Methods for Non-Linear Variational Problems

The classical problem of solving an nth degree polynomial equation has substantially influenced the development of mathematics throughout the centuries and still has several important applications to the theory and practice of present-day computing. We briefly recall the history of the algorithmic approach to this problem and then review some successful solution algorithms. We end by outlining some algorithms of 1995 that solve this problem at a surprisingly low computational cost.

The numerical treatment of a single nonlinear equation

Citations

An introduction to numerical analysis

Lectures on Numerical Methods for Non-Linear Variational Problems

Solving a Polynomial Equation: Some History and Recent Progress

Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method

On the partial realization problem

Related Papers (5)

Applied and Computational Complex Analysis

Iterative Methods for the Solution of Equations

Solution of equations and systems of equations

Matrix computations

Introduction to Numerical Analysis