Basic Tools for Linear Algebra

In this chapter we discuss how object-oriented techniques can be applied in the design and implementation of a software library for linear algebra computations. 1.1 Introduction The basic concepts in linear algebra, such as vectors and matrices, are of fundamental importance to most applications in applied mathematics. This statement is indeed valid for the numerical solution of partial differential equations, and yet applicable to problems from quite different origins, such as in data approximation or in relation to economical and statistical models. For this reason, the design of a flexible and comprehensive linear algebra toolkit is vital to large-scale development of scientific software. In this chapter we will address important issues concerning the design of such a toolkit within the framework of object-oriented programming (OOP), see [2, 4, 12] and references therein. To a large extent, we discuss possible solutions that have been implemented in C++ as part of Diffpack [7,8,..