On the Average Errors of Multivariate Lagrange Interpolation

On the Average Errors of Multivariate Lagrange Interpolation

On Multivariate Lagrange Interpolation

Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...

A continuity property of multivariate Lagrange interpolation

Let {St} be a sequence of interpolation schemes in Rn of degree d (i.e. for each St one has unique interpolation by a polynomial of total degree ≤ d) and total order ≤ l. Suppose that the points of St tend to 0 ∈ Rn as t→ ∞ and the Lagrange-Hermite interpolants, HSt , satisfy limt→∞HSt(x) = 0 for all monomials xα with |α| = d + 1. Theorem: limt→∞HSt (f) = T d(f) for all functions f of class Cl−...

the effect of consciousness raising (c-r) on the reduction of translational errors: a case study

در دوره های آموزش ترجمه استادان بیشتر سعی دارند دانشجویان را با انواع متون آشنا سازند، درحالی که کمتر به خطاهای مکرر آنان در متن ترجمه شده می پردازند. اهمیت تحقیق حاضر مبنی بر ارتکاب مکرر خطاهای ترجمانی حتی بعد از گذراندن دوره های تخصصی ترجمه از سوی دانشجویان است. هدف از آن تاکید بر خطاهای رایج میان دانشجویان مترجمی و کاهش این خطاها با افزایش آگاهی و هوشیاری دانشجویان از بروز آنها است.از آنجا ک...

Intertwining unisolvent arrays for multivariate Lagrange interpolation

Let Pd(C ) denote the space of polynomials of degree at most d in n complex variables. A subset X of C – we will usually speak of configuration or array – is said to be unisolvent for Pd(C ) (or simply unisolvent of degree d) if, for every function f defined on X there exists a unique polynomial P ∈ Pd(C ) such that P(x) = f (x) for every x ∈ X. This polynomial is called the Lagrange interpolat...