NUMERICAL ANALYSIS. AN ADVANCED COURSE

Numerical Analysis is a branch of Mathematics which deals with the constructive solutions of many problems formulated and studied by other fields of Mathematics. As illustrative examples, one may consider the problem of solving operatorial equations, the polynomial approximation of real-valued functions, the numerical integration of functions, and so on. At the same time, Numerical Analysis has a theoretical aspect of its own. When analyzing a numerical method, one studies the error for the numerical solution, and obtains results concerning convergence and error bounds. This book provides both theoretical and numerical aspects for basic problems of Numerical analysis, with a special emphasis and optimal approximation. It is addressed, first of all, to the undergraduate students, master students and Ph. D students in Mathematics, but also to the students of Computer Science, Engineering, and to all the people intrested in Numerical Analysis and Approximation Theory.