Notes on Polynomial Interpolation 2D1250, Tillämpade numeriska metoder II
نویسنده
چکیده
f(xj) = p(xj), j = 1, . . . , n. This is sometimes called Lagrange interpolation to distinguish it from Hermite interpolation, see below. For the basics, see Chapter 7 in Heath. As in Heath, we let Pn be the (function) space of polynomials of degree at most n. We let C([a, b]) denote the set of continuous functions on the interval [a, b]. Similarly, we let C([a, b]) be the n times continuously differentiable functions on [a, b].
منابع مشابه
Part III: Polynomial-Based Interpolation for DSP Applications
Part III: Polynomial-Based Interpolation for DSP Applications • This pile of lecture notes is mainly based on the research work done by Jussi Vesma and the lecturer during the last three years. • Many thanks to Jussi Vesma for his help in preparing this pile of lecture notes. • If there is some interest to get the pile of lecture notes of the overall course, please contact Tapio Saramäki using ...
متن کاملgH-differentiable of the 2th-order functions interpolating
Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...
متن کاملAdditional Notes on Polynomial GCDs, Hensel construction
These notes cover a number of topics that are covered in any of the typical texts. We provide this discussion here to try to touch on some of the highlights and offer some perspective. First we demonstrate that interpolation can be done as a special case of Garner's Algorithm by appropriately choosing our (relatively prime) moduli. As an example, we choose the moduli m i , to be linear polynomi...
متن کاملHigh order summation-by-parts methods in time and space
This thesis develops the methodology for solving initial boundary value problems with the use of summation-by-parts discretizations. The combination of high orders of accuracy and a systematic approach to construct provably stable boundary and interface procedures makes this methodology especially suitable for scientific computations with high demands on efficiency and robustness. Most classes ...
متن کاملPolynomial Interpolation
Consider a family of functions of a single variable x: Φ(x; a0, a1, . . . , an), where a0, . . . , an are the parameters. The problem of interpolation for Φ can be stated as follows: Given n + 1 real or complex pairs of numbers (xi, fi), i = 0, . . . , n, with xi 6= xk for i 6= k, determine a0, . . . , an such that Φ(xi; a0, . . . , an) = fi, i = 0, . . . , n. The above is a linear interpolatio...
متن کامل