Application of almost‐everywhere singular distributions in chemical engineering

Giona, Massimiliano; Patierno, Oreste

doi:10.1002/aic.690430616

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2000

2008

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“…105ff.). The Stieltjes integral occurs in numerous areas, such as biology (Louie and Somorjai, 1984), chemistry (Cacelli et al, 1988) chemical engineering (Giona and Patierno, 1997), finance (Duffie, 1996), nuclear engineering (Akiba et al, 1996) physics (Avellaneda and Vergassola, 1995), and stochastic differential equations (Revuz and Yor, 1994).…”

Section: Introductionmentioning

confidence: 99%

What Is the Complexity of Stieltjes Integration?

Werschulz¹

2000

Journal of Complexity

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We study the complexity of approximating the Stieltjes integral 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 n th 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) Ä n &min [r, s+1] and that comp(=) Ä = &1Âmin [r, s+1] . We also present an algorithm that computes an =-approximation at nearly minimal cost. AcademicPress

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