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Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions
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A simple method is proposed for constructing fourth-degree cubature
formulae over general product regions with no symmetric assumptions.
The cubature formulae that are constructed contain at most $n^2+7n+3$ nodes and they are likely the first kind of fourth-degree
cubature formulae with roughly $n^2$ nodes for non-symmetric
integrations. Moreover, two special cases are given to reduce the
number of nodes further. A theoretical upper bound for minimal
number of cubature nodes is also obtained.
Title: Simple Fourth-Degree Cubature Formulae with Few Nodes over General Product Regions
Description:
A simple method is proposed for constructing fourth-degree cubature
formulae over general product regions with no symmetric assumptions.
The cubature formulae that are constructed contain at most $n^2+7n+3$ nodes and they are likely the first kind of fourth-degree
cubature formulae with roughly $n^2$ nodes for non-symmetric
integrations.
Moreover, two special cases are given to reduce the
number of nodes further.
A theoretical upper bound for minimal
number of cubature nodes is also obtained.
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