# FAST ALGORITHMS TO COMPUTE MATRIX-VECTOR PRODUCTS FOR PASCAL MATRICES

 Title FAST ALGORITHMS TO COMPUTE MATRIX-VECTOR PRODUCTS FOR PASCAL MATRICES Publication Type Journal Articles Year of Publication 2004 Authors Tang Z, Duraiswami R, Gumerov NA Journal Technical Reports from UMIACS UMIACS-TR-2004-08 Date Published 2004/03/25/ Keywords Technical Report Abstract The Pascal matrix arises in a number of applications. We present a few waysto decompose the Pascal matrices of size $n \times n$ into products of matrices with structure. Based on these decompositions, we propose fast algorithms to compute the product of a Pascal matrix and a vector with omplexity $O(n\log n)$. We also present a strategy to stabilize the proposed algorithms. Finally, we also present some interesting properties of the Pascal matrices that help us to compute fast the product of the inverse of a Pascal matrix and a vector, and fast algorithms for generalized Pascal Matrices. UMIACS-TR-2004-08 URL http://drum.lib.umd.edu/handle/1903/1338