Computational complexity on numerical integrals (Q1177970)
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scientific article; zbMATH DE number 22585
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Computational complexity on numerical integrals |
scientific article; zbMATH DE number 22585 |
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Computational complexity on numerical integrals (English)
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26 June 1992
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This paper analyzes the computational complexity of one-dimensional integration formulas. The authors generalize some earlier work by Smale in this area. Their main result is an explicit formula for the expected error from a degree \(k-1\) quadrature formula, with the average taken over functions in an appropriate Sobolev space. Exact error constants for the midpoint, trapezoidal and Simpson formulas are given.
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midpoint formula
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trapezoidal formula
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computational complexity
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one- dimensional integration
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quadrature formula
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Sobolev space
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Simpson formulas
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