We propose an efficient algorithm for computing a unit lower triangular n×n matrix with prescribed singular values of O(n 2) cost. This is a solution of the question raised by N. J. Higham in [4,… (More)

An error analysis result is given for classical Gram–Schmidt factorization of a full rank matrix A into A = QR where Q is left orthogonal (has orthonormal columns) and R is upper triangular. The work… (More)

A reorthogonalized block classical Gram–Schmidt algorithm is proposed that factors a full column rank matrix A into A = Q R where Q is left orthogonal (has orthonormal columns) and R is upper… (More)

In this paper we study the numerical properties of several orthogonalization schemes where the inner product is induced by a nontrivial symmetric and positive definite matrix. We analyze the effect… (More)

It is known that Goertzel’s algorithm is much less numerically accurate than the Fast Fourier Transform (FFT) (cf. [2]). In order to improve accuracy we propose modifications of both Goertzel’s and… (More)

The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Björck… (More)

A new backward stable algorithm (Algorithm 2) for polynomial interpolation based on the Lagrange and the Newton interpolation forms is proposed. It is shown that the Aitken algorithm and the scheme… (More)

Received by the editors on July 14, 2010. Accepted for publication on October 5, 2011. Handling Editor: Richard Brualdi. Faculty of Mathematics and Information Science, Warsaw University of… (More)