Introduction to Precise Numerical Methods

Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented.

· Clearer, simpler descriptions and explanations of
the various numerical methods
· Two new types of numerical problems; accurately
solving partial differential equations with the included software and computing line integrals in the complex plane.

Beginning classes in Numerical Analysis taught out of Computer Science or Engineering Departments. Also Math Departments where it is taught to students of other disciplines. European technical schools and universities, especially Germany, would have strong interest in a book on interval arithmetic. The guaranteed accuracy of this software makes it very desirable for engineers and scientists who need to solve numerical problems in their work

Preface; 1 Introduction; 2 Computer Arithmetics; 3 Classification of Numerical Computation Problems; 4 Real-Valued Functions; 5 Computing Derivatives; 6 Computing Integrals; 7 Finding Where a Function f(x) is Zero; 8 Finding Roots of Polynomial; 9 Solving n Linear Equations in n Unknowns; 10 Eigenvalue and Eigenvector Problems; 11 Problems of Linear Programming; 12 Finding Where Several Functions are Zero; 13 Optimization Problems; 14 Ordinary Differential Equations; 15 Partial Differential Equations; 16 Numerical Methods with Complex Functions; Index