Error Bounds for the Numerical Integration of Functions with Limited Smoothness

Bounds for smoothness of refinable functions

The VILLEMOES machine can be used to compute the SOBOLEV smoothness of a refinable function. We start with presenting this technique. It involves the computation of the spectral radius of a special matrix which has at least quadratic time complexity with respect to the refinement mask size. For the one-dimensional case we deduce by linear algebra some simple estimates which require only a few b...

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.

A Numerical Integration Method by Using Generalized Series of Functions

Error bounds for kernel-based numerical differentiation

The literature on meshless methods observed that kernel-based numerical differentiation formulae are robust and provide high accuracy at low cost. This paper analyzes the error of such formulas, using the new technique of growth functions. It allows to bypass certain technical assumptions that were needed to prove the standard error bounds on interpolants and their derivatives. Since differenti...

Error bounds for quasi-Monte Carlo integration with nets

We analyze the error introduced by approximately calculating the s-dimensional Lebesgue measure of a Jordan-measurable subset of Is = [0, 1)s. We give an upper bound for the error of a method using a (t,m, s)-net, which is a set with a very regular distribution behavior. When the subset of Is is defined by some function of bounded variation on Īs−1, the error is estimated by means of the variat...