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- W2325196662 abstract "We develop an extrapolation algorithm for numerical integration over arbitary non-standard triangles in IR², which parallels the well-known univariate Romberg method. This is done by a suitable generalization of the trapezoidal rule over triangles, for which we can prove the existence of an asymptotic expansion. Our approach relies mainly on two ideas: The use of barycentric coordinates and the interpretation of the trapezoidal rule as the integral over an interpolating linear spline function. Since our method works for arbitrary triangles, it yields - via triangulation - a method for cubature over arbitrary, possibly non-convex, polygon regions in IR². Moreover, also numerical integration over convex polyhedra in IR d, d > 2 , can be accomplished without difficulties. Numerical examples show the stability and efficiency of the algorithm." @default.
- W2325196662 created "2016-06-24" @default.
- W2325196662 creator A5083010820 @default.
- W2325196662 date "1997-01-01" @default.
- W2325196662 modified "2023-09-27" @default.
- W2325196662 title "Romberg Type Cubature over Arbitrary Triangles" @default.
- W2325196662 hasPublicationYear "1997" @default.
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