The complexity of accurate floating point computation
James Demmel
Abstract
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational expressions as entries. More precisely, accuracy means the relative error in the output must be less than one (no matter how tiny the output is), and efficiency means that the algorithm runs in polynomial time. Our goal is challenging because our accuracy demand is much stricter than usual.
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