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On Roundoff Error Growth in Elliptic Problems
ACM Transactions on Mathematical Software, 2018Large-scale linear systems arise in finite-difference and finite-element discretizations of elliptic problems. With increasing computer performance, ever larger systems are solved using direct methods. How large can such systems be without roundoff compromising accuracy? Here we model roundoff dynamics in standard LU
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Limit distribution of a roundoff error
Statistics & Probability Letters, 2012Denote by \([x]:=\sup\{m\in\mathbb{Z}:\,m\leq x\}\) the integral part of \(x\in\mathbb{R}\) and by \(\{x\}:=x-[x]\in[0,1)\) its fractional part. Let \(X\) be a random variable. The conditional distribution function \(F_n(x):=P(\{X\}\leq x \mid [X]=n)\) for an integer \(n\in\mathbb{N}\) is investigated. Characterizations of the limit of \(F_n\) when \(n\
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