POLYNOMIAL BASIS CONVERSION MADE STABLE BY TRUNCATED SINGULAR-VALUE DECOMPOSITION

The transformations between the power and Bernstein polynomial bases, and the Bernstein and B-spline polynomial bases, are defined by a line ar algebraic equation whose coefficient matrix is square and nonsingul ar. Direct solution of the equation is not always recommended because it may be ill-conditioned. This paper considers the use of truncated s ingular value decomposition for the regularisation of the equation. An important consideration in this method is the deletion of the correct number of singular values of the coefficient matrix and a method that enables this number to be determined is described Examples of the use of truncated singular value decomposition far both transformations ar e presented. (C) 1997 by Elsevier Science Inc.