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Polynomials are widely used in scientific computing and engineering. In this paper, we present an accurate and fast compensated algorithm to evaluate bivariate polynomials with floating-point coefficients. This algorithm is applying error free transformations to the bivariate Horner scheme and sum the final decomposition accurately. We also prove the… (More)
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)
Designing fast singular value decomposition (SVD) is significantly interesting in applications. The random direct SVD (RSVD) has provided a fast scheme to compute the well-approximate SVD by unilateral randomized sampling. In this paper, we present an efficient random algorithm in a bilateral sampling way. We also prove that the proposed algorithms can be… (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.