What is the complexity of Stieltjes integration ? Arthur
نویسنده
چکیده
We study the complexity of approximating the Stieltjes integral R 1 0 f (x) dg(x) for functions f having r continuous derivatives and functions g whose sth derivative has bounded variation. Let r(n) denote the nth minimal error attainable by approximations using at most n evaluations of f and g, and let comp(") denote the "-complexity (the minimal cost of computing an "-approximation). We show that r(n) n ? minfr;s+1g and that comp(") " ?1= minfr;s+1g. We also present an algorithm that computes an "-approimation at nearly-minimal cost.
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What Is the Complexity of Stieltjes Integration?
We study the complexity of approximating the Stieltjes integral R 1 0 f (x)dg(x) for functions f having r continuous derivatives and functions g whose sth derivative has bounded variation. Let r(n) denote the nth minimal error attainable by approximations using at most n evaluations of f and g, and let comp(ε) denote the ε-complexity (the minimal cost of computing an ε-approximation). We show t...
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