A quadrature formula associated with a univariate spline quasi interpolant
نویسندگان
چکیده
منابع مشابه
A quadrature formula associated with a univariate quadratic spline quasi-interpolant
We study a new simple quadrature rule based on integrating a C1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions and we compare this formula with Simpson’s rule.
متن کاملThe quasi–interpolant as a tool in elementary polynomial spline theory
taking, for each fixed t, the k divided difference of g(s) := gk(s; t) at ti, . . . ti+k in the usual manner even when some or all of the tj ’s coincide. I leave unresolved any possible ambiguity when t = tj for some j, and concern myself only with left and right limits at such a point; i.e., I replace each t = tj by the “two points” tj and t + j . As is well known, Nik > 0 on (ti, ti+k), and N...
متن کاملUnivariate Spline Quasi - Interpolants and Applications to Numerical Analysis
We describe some new univariate spline quasi-interpolants on uniform partitions of bounded intervals. Then we give some applications to numerical analysis: integration, differentiation and approximation of zeros.
متن کاملTwelfth degree spline with application to quadrature
In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order [Formula: see text] that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applica...
متن کاملA corrected quadrature formula and applications
A straightforward 3-point quadrature formula of closed type is derived that improves on Simpson’s rule. Just using the additional information of the integrand’s derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2007
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-007-0146-8