'A PRIORI' KNOWLEDGE, NON-ORTHOGONAL BASIS FUNCTIONS, AND ILL-CONDITIONNED MATRICES IN NUMERICAL METHODS

Abstract

Many terms and ideas used in numerical methods have their origin in analytical mathematics. Despite the well-known discrepancies between number spaces of computers and those of good old mathematics, the consequences of applying mathematical theorems to numerical methods and the importance of physical reasoning are often underestimated. The objective of this paper is to demonstrate that introducing 'a priori' knowledge of a problem into a numerical code can lead to superior numerical techniques but it may violate analytic dogmas at the same time. [Vol. 8, No. 2 (1993), pp 176-187]