ABSTRACT
One of the commonest numerical tasks facing engineers is the solution of sets of linear algebraic equations of the form,
a11x1 + a12x2 + a13x3 = b1 a21x1 + a22x2 + a23x3 = b2 (2.1) a31x1 + a32x2 + a33x3 = b3
commonly written [A]{x} = {b} (2.2)
where [A] is a “matrix” and {x} and {b} are “vectors”. In these equations the aij are constant known quantities, as are the bi. The
problem is to determine the unknown xi. In this chapter we shall consider two different solution techniques, usually termed “direct” and “iterative” methods. The direct methods are considered first and are based on row by row “elimination” of terms, a process usually called “Gaussian elimination”.
