Title: Fast and Stable Pascal Matrix Algorithms,
Abstract: In this paper, we derive a family of fast and stable algorithms for
multiplying and inverting $n \times n$ Pascal matrices that run in $O(n log^2
n)$ time and are closely related to De Casteljau's algorithm for Bézier curve
evaluation. These algorithms use a recursive factorization of the triangular
Pascal matrices and improve upon the cripplingly unstable $O(n log n)$ fast
Fourier transform-based algorithms which involve a Toeplitz matrix
factorization. We conduct numerical experiments which establish the speed and
stability of our algorithm, as well as the poor performance of the Toeplitz
factorization algorithm. As an example, we show how our formulation relates to
Bézier curve evaluation.