Alicja Smoktunowicz

Backward Stability of Clenshaw's Algorithm

We study numerical properties of Clenshaws algorithm for summing the series w = ∑n = 0Nbnpn where pn satisfy the linear three-term recurrence relation. We prove that under natural assumptions Clenshaws algorithm is backward stable with respect to the data bn, n = 0,N.

On constructing unit triangular matrices with prescribed singular values

Abstract We propose an efficient algorithm for computing a unit lower triangular n×n matrix with prescribed singular values of O(n2) cost. This is a solution of the question raised by N. J. Higham in [4, Problem 26.3, p. 528].

Reorthogonalized block classical Gram---Schmidt

A reorthogonalized block classical Gram–Schmidt algorithm is proposed that factors a full column rank matrix

The three-term recursion for Chebyshev polynomials is mixed forward-backward stable

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A new efficient algorithm for polynomial interpolation

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Forward Stability of Iterative Refinement with a Relaxation for Linear Systems

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