Add to ORKGLet M (f) denote the midpoint rule and T (f) the trapezoidal rule for estimating ∫ b a f(x) dx. Then Simpson’s rule =M (f) + (1 − )T (f), where = 23. We generalize Simpson’s rule to multiple integrals as follows. Let Dn be some polygonal region in Rn; let P0; : : : ; Pm denote the vertices of Dn, and let Pm+1 equal the center of mass of Dn. De4ne the linear functionals M (f) =Vol(Dn)f(Pn+1), which generalizes the midpoint rule, and T (f) =Vol(Dn)([1=(m
High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and c...
Fully symmetric interpolatory integration rules are constructed for multidimensional inte-grals over...
Zero divided by zero is arguably the most important concept in calculus, as it is the gateway to the...
AbstractLet M(f) denote the midpoint rule and T(f) the trapezoidal rule for estimating ∫abf(x)dx. Th...
Abstract. An interesting property of the midpoint rule and trapezoidal rule, which is expressed by t...
When it is not possible to integrate a function we resort to Numerical Integration. For example the ...
A generalization of the modified Simpson's rule is derived. Various error bounds for this generaliz...
International audienceIf $I_n$ is the approximation of a definite integral $\int_{a}^{b}f(x)dx$ with...
The article investigates interior point rules which contain the midpoint as a special case, and obta...
A unified treatment of three point quadrature rules is presented in which the classical rules of mid...
A unified treatment of three point quadrature rules is presented in which the classical rules of mid...
This paper reviews recent work on numerical multiple integration over the d- dimensional unit cube ...
AbstractWe obtain Midpoint and Trapezoid Rules for the Riemann–Stieltjes integral which engender a n...
If In is the approximation of a definite integral with step using the trapezoidal rule (respective...
Some new inequalities are obtained relating to the generalized trapezoid and midpoint rules for the ...
High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and c...
Fully symmetric interpolatory integration rules are constructed for multidimensional inte-grals over...
Zero divided by zero is arguably the most important concept in calculus, as it is the gateway to the...
AbstractLet M(f) denote the midpoint rule and T(f) the trapezoidal rule for estimating ∫abf(x)dx. Th...
Abstract. An interesting property of the midpoint rule and trapezoidal rule, which is expressed by t...
When it is not possible to integrate a function we resort to Numerical Integration. For example the ...
A generalization of the modified Simpson's rule is derived. Various error bounds for this generaliz...
International audienceIf $I_n$ is the approximation of a definite integral $\int_{a}^{b}f(x)dx$ with...
The article investigates interior point rules which contain the midpoint as a special case, and obta...
A unified treatment of three point quadrature rules is presented in which the classical rules of mid...
A unified treatment of three point quadrature rules is presented in which the classical rules of mid...
This paper reviews recent work on numerical multiple integration over the d- dimensional unit cube ...
AbstractWe obtain Midpoint and Trapezoid Rules for the Riemann–Stieltjes integral which engender a n...
If In is the approximation of a definite integral with step using the trapezoidal rule (respective...
Some new inequalities are obtained relating to the generalized trapezoid and midpoint rules for the ...
High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and c...
Fully symmetric interpolatory integration rules are constructed for multidimensional inte-grals over...
Zero divided by zero is arguably the most important concept in calculus, as it is the gateway to the...