This book can be strongly recommended not only to students interested in the field, but also to mathematicians collaborating with non-mathematicians in research or hard practice, moreover to engineers, physicists and other natural scientists needing effective methods in scientific computing and wanting to know their underlying theory. The authors present the treated topics in a convincing synthesis of theory and practice, with well-chosen motivating examples, and when appropriate for understanding the principles not shying away from giving occasional proofs, use of basic functional-analytic concepts (like norms) and other analytical tools. They lay emphasis on complexity considerations (as important for efficient applicability) of methods, furthermore on questions of accuracy (via condition numbers) and stability. Many exercises offer the student the opportunity to gain more insight and to aquire a solid working knowledge. For useful algorithms written in MATLAB a web page is offered. To give a rough overview on the scope of the book let us look into the list of contents. Ch. 1: Mathematical review and computer arithmetic. Ch. 2: Numerical solution of nonlinear equations of one variable. Ch. 3: Numerical linear algebra. Ch. 4: Approximation theory. Ch. 5: Eigenvalue-eigenvector computation. Ch. 6: Numerical differentiation and integration. Ch. 7: Initial value problems for ordinary differential equations. Ch. 8: Numerical solution of systems of nonlinear equations. Ch. 9: Optimization. Ch. 10: Boundary-value problems and integral equations.
Reviewer: Rudolf Gorenflo (Berlin)