Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
Generalized Gaussian quadrature rules for systems of arbitrary functions
SIAM Journal on Numerical Analysis
Anti-Gaussian quadrature formulas
Mathematics of Computation
Computation of Gauss-type quadrature formulas
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Orthogonal polynomials and Gaussian quadrature rules related to oscillatory weight functions
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
MAASE'08 Proceedings of the 1st WSEAS International Conference on Multivariate Analysis and its Application in Science and Engineering
MAASE'08 Proceedings of the 1st WSEAS International Conference on Multivariate Analysis and its Application in Science and Engineering
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According to the fluctuationlessness theorem the matrix representation of a function can be approximated by the image of independent variable operator's matrix representation under that function. The independent variable operator's action is defined as the multiplication of the operand by the independent variable. Hence itself and therefore its matrix representation is universal, do not depend on the function. The application of this approximation to numerical integration forms a quadrature whose structure can be manipulated by changing the basis set of an n-dimensional Hilbert space. This work focuses on reflecting the effects of a complementary Hilbert space to a restricted Hilbert subspace by forming the basis set as certain linear combinations of some basis functions in order to improve the accuracy of the numerical integration based on fluctuationlessness theorem.