This article describes a Matlab implementation of a mixed extended-precision package with three multiple-component formats. In the package, double-double, triple-double, and quad-double numbers, which are unevaluated sums of two, three and four IEEE double precision numbers respectively, are defined as Matlab classes including real and complex formats. We… (More)
We present a compensated algorithm to evaluate the first derivative of B'ezier tensor product surface in floating arithmetic. The algorithm based on error-free transformation is fast in terms of measured computing time, and the computed results are as accurate as the classic de Casteljau tensor product algorithm in twice the working precision. We also… (More)
This paper presents three accurate methods for finding simple roots of polynomials in floating point arithmetic. We present them by using the Compensated Horner algorithm to accurately compute the residual which can yield a full precision when the problem is ill-conditioned enough. Some numerical experiments are conducted to justify the proposed approaches.