ABSTRACT
Linearization is a common assumption or approximation in describing physical processes and so linear systems of equations are ubiquitous in computational physics. Indeed, the matrix manipulations associated with finding eigenvalues or with solving simultaneous linear equations are often the bulk of the work involved in solving many physical problems. In this chapter, we will discuss briefly two of the more non-trivial matrix opera tions: inversion and diagonalization. Our treatment here will be confined largely to “direct” methods appropriate for “dense” matrices (where most of the elements are non-zero) of dimension less than several hundred; it erative methods for treating the very large sparse matrices that arise in the discretization of ordinary and partial differential equations will be discussed in the following two chapters. As is the case with the special functions of the previous chapter, a variety of library subroutines em ploying several different methods for solving matrix problems are usually available on any large computer. Our discussions here are therefore lim ited to selected basic methods, to give a flavor of what has to be done. More detailed treatments can be found in many texts, for example [Ac70] and [Bu81].
