2022年5月31日 · Here, we use \(n\) piecewise cubic polynomials for interpolation, \[g_{i}(x)=a_{i}\left(x-x_{i}\right)^{3}+b_{i}\left(x-x_{i}\right)^{2}+c_{i}\left(x-x_{i}\right)+d_{i}, \quad i=0,1, \ldots, n-1, \nonumber \]

2021年7月18日 · Cubic spline interpolation is a way of finding a curve that connects data points with a degree of three or less. Splines are polynomial that are smooth and continuous across a given plot and also continuous first and second derivatives where they join.

In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the ...

2023年11月11日 · Cubic spline interpolation is a special case for Spline interpolation that is used very often to avoid the problem of Runge's phenomenon. This method gives an interpolating polynomial that is smoother and has smaller error than some other interpolating polynomials such as Lagrange polynomial and Newton polynomial .

Cubic Spline Interpolation¶ In cubic spline interpolation (as shown in the following figure), the interpolating function is a set of piecewise cubic functions. Specifically, we assume that the points \((x_i, y_i)\) and \((x_{i+1}, y_{i+1})\) are joined by a cubic polynomial \(S_i(x) = a_i x^3 + b_i x^2 + c_i x + d_i\) that is valid for \(x_i ...

2023年10月12日 · This post explains how cubic spline interpolation works, and presents a full implementation in JavaScript, hooked up to a SVG-based visualization. As a side effect, it also covers Gaussian elimination and presents a JavaScript implementation of that as well.

The method of approximation we describe is called cubic spline interpolation. The cubic spline is a function S(x) on [a;b] with the following properties. S(x) [x i;x i+1] = S i(x) is a cubic polynomial for i = 0;1;2;:::;n 1 S i(x i) = f(x i) for i = 0;1;2;:::;n 1 S i(x i+1) = f(x i+1) for i = 0;1;2;:::;n 1 S0 i (x i+1) = S 0 i+1 (x i+1) for i ...

Cubic spline data interpolator. Interpolate data with a piecewise cubic polynomial which is twice continuously differentiable . The result is represented as a PPoly instance with breakpoints matching the given data. Parameters: x array_like, shape (n,) 1-D array containing values of the independent variable.

The goal of cubic spline interpolation is to get an interpolation formula that is smooth in the first derivative, and continuous in the second derivative, both within an interval and at its boundaries.

Cubic Spline we want to construct a cubic spline S(x) to interpolate the table presumable of a function f(x). We assume that the points are ordered so that a = t 0 < t 1 < ··· < t N = b. S(x) is given by a different cubic polynomial in each interval [t 0,t 1], [t 1,t 2], ···, [t N−1,t N]. Let S ( x) be given by i) if ∈ [t ,t +1 ...