i=0 if(xi): (2) i.e., we express the numerical approximation to the integral I(f) as a sum of a series of nite number of terms, each term containing the value of the function at a given point xi weighted by a coe cient i. One way to determine the coe cients i is to replace the original function f(x) by an interpolating function which is simple enough, or in the terminology of numerical analysts...

1. General Introduction. Numerical analysis is the area of mathematics and computer science that creates, analyzes, and implements algorithms for solving numerically the problems of continuous mathematics. Such problems originate generally from real-world applications of algebra, geometry and calculus, and they involve variables which vary continuously; these problems occur throughout the natur...

We review the present status of the null cone approach to numerical evolution being developed by the Pittsburgh group. We describe the simplicity of the underlying algorithm as it applies to the global description of general relativistic spacetimes. We also demonstrate its effectiveness in revealing asymptotic physical properties of black hole formation in the gravitational collapse of a scalar...

Binary morphological transformations based on the residues (ultimate erosion, skeleton by openings, etc.) are extended to functions by means of the transformation definition and of its associated function based on the analysis of the residue evolution in every point of the image. This definition allows to build the transformed image and its associated function, indicating the value of the resid...

Current methods to index and retrieve documents from databases usually depend on a lexical match between query terms and keywords extracted from documents in a database. These methods can produce incomplete or irrelevant results due to the use of synonyms and polysemus words. The association of terms with documents (or implicit semantic structure) can be derived using large sparse term-by-docum...

The strong coupling expansion coefficients for the ordinary and renormalized energies of the ground and first excited states of the quartic, sextic, octic and decadic anharmonic oscillators with the Hamiltonian 2 + 2 + 2 , 2 3 4 5 are computed. The expansion coefficients are also computed for higher excited states of the quartic oscillator. The large-order beha viour of the coefficients, the ra...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

This article focuses on the process of approximating a definite integral from values of the integrand when exact mathematical integration is not available. This problem arises in statistics when marginal density functions or expected values of random variables are required. The article describes classical univariate quadrature methods including the trapezoidal rule, Simpson’s rule, Newton-Cotes...

Numerical analysis is concerned with the accurate and eecient evaluation of mathematical expressions, especially on computers with oating point arithmetic. While scientists have always been concerned to some extent with numerical computation, the modern discipline of numerical analysis is almost entirely a product of the period since 1950 during which there has been an explosion in the availabi...