@MISC{By_lanumerical, author = {Copyright By}, title = {LA Numerical Linear Algebra}, year = {} }

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Abstract

Introduction We begin with an example to motivate our study of parallel and vector algorithms for linear algebra problems. Consider solving a system of linear equations Ax = b, where A is a given dense n-by-n matrix, b is a given n-by-1 vector, and x is an n-by-1 vector of unknowns we want to compute. The algorithm we will use is Cholesky, which is a variation of Gaussian elimination suitable for matrices A with the special (but common) properties of symmetry and positive definiteness (these are discussed in more detail below). Cholesky, as well as Gaussian elimination, consists almost entirely of simple, regular operations which are in principle easy to parallelize or vectorize: adding multiples of one column of the matrix to other columns. Since vector processors like the Cray Y-MP are designe