Gaussian Quadrature as a Numerical Integration Method for Estimating Area Under the Curve.

Numerical integration over a disc. A new Gaussian quadrature formula

The ordinary type of information data for approximation of functions f or functionals of them in the univariate case consists of function values {f(x1), . . . , f(xm)}. The classical Lagrange interpolation formula and the Gauss quadrature formula are famous examples. The simplicity of the approximation rules, their universality, the elegancy of the proofs and the beauty of these classical resul...

The Gaussian Quadrature Method

Numerical Construction of Gaussian Quadrature Formulas for

Most nonclassical Gaussian quadrature rules are difficult to construct because of the loss of significant digits during the generation of the associated orthogonal polynomials. But, in some particular cases, it is possible to develop stable algorithms. This is true for at least two well-known integrals, namely ¡l-(Loêx)-x°f(x)dx and ¡Ô Em(x)f(x)-dx. A new approach is presented, which makes use ...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Area under the curve as a measure of discounting.

We describe a novel approach to the measurement of discounting based on calculating the area under the empirical discounting function. This approach avoids some of the problems associated with measures based on estimates of the parameters of theoretical discounting functions. The area measure may be easily calculated for both individual and group data collected using any of a variety of current...