On the numerical solution of non-linear equation characterizing minimal cubature formulae
Copyright policy )On the numerical solution of non-linear equation characterizing minimal cubature formulae
A cubature formula with degree of exactness ≦2k−2 has at leastk(k+1)/2 knots. The existence of such minimal formulae is equivalent to the existence of solutions of a system of quadratic equations. Each solution of such a system generates in a uniquely determined way a minimal formula. For the square [−1, 1]2 as domain of integration and for some weight-functions these systems have a simple form, but they seem to be hard to solve. In this note attention is drawn to these systems and to experiences made in order to obtain numerical solutions.
- University of Bonn Germany
Numerical computation of solutions to systems of equations, Multidimensional problems, system of quadratic equations, Numerical quadrature and cubature formulas, Approximate quadratures, minimal cubature formulae
Numerical computation of solutions to systems of equations, Multidimensional problems, system of quadratic equations, Numerical quadrature and cubature formulas, Approximate quadratures, minimal cubature formulae
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