elative Error P r o p a g a t i o n in the R e c u r s i v e S o l u t i o n下载

An important method for the systematic evaluation of functions obeying a linear recurrence relation with respect to one of their parameters is to solve the relation recursively, making use of known initial values. The necessity of solving such initial value problems can arise in other contexts, such as in the numerical solution of differential equations. As is well known, the accumulation of errors due to inexact starting values and to rounding can sometimes prevent any useful accuracy from being obtained in the computed solution, unless a prohibitively large number of guarding figures is used. Thus an obvious need exists to determine those circumstances in which the accumulation of errors can present a serious computational problem, and to develop alternative methods of solution which avoid this unpleasant error behaviour.