一般有三种边界条件:自然边界(Natural Spline),固定边界(Clamped Spline),非节点边界(Not-A-Knot Spline)。 - 自然边界 指定端点二阶导数为0,即S^{''}_0(x_0) = S^{''}_{n-1}(x_n)=0。 固定边界 人为指定端点一阶导数,这里分别定为A和B,即S^{'}_0(x_0) = A, S^{'}_{n-1}(x_n)...
tmp = (B[i] - A[i] * C[i-1]); C[i] = C[i] / tmp; D[i] = (D[i] - A[i] * D[i-1]) / tmp; } //直接求出X的最后一个值 X[n-1] = D[n-1]; //逆向迭代, 求出X for(i = n-2; i>=0; i--) { X[i] = D[i] - C[i] * X[i+1]; }}#define MDL...
其中,Pi(t)多项式中最高次项的幂,视为样条的阶数或次数(Order of spline),根据子区间[ti−1,ti]的区间长度是否一致分为均匀(Uniform)样条和非均匀(Non-uniform)样条。满足了公式(2)的多项式有很多,为了保证曲线在S区间内具有据够的平滑度,一条n次样条,同时应具备处处连续且可微的性质: P(j)i(ti)=P(...
b. 满⾜（i = 0, 1, …, n ）c. ，导数，⼆阶导数在[a, b]区间都是连续的，即曲线是光滑的。所以n个三次多项式分段可以写作：，i = 0, 1, …, n-1 其中ai, bi, ci, di代表4n个未知系数。1.2 求解 已知:a. n+1个数据点[xi, yi], i = 0, 1, …, n b. 每⼀分段都是...
5) double periodic quadratic spline space 双周期二次样条空间 1. Define S21(△mn(i))={s∈S21(△mn(i)):Das(·,0)=Das(·,yn),Das(0,·)=Das(Xm,·),a=0,1},called double periodic quadratic spline space. 本文给出了Ω的非均匀(Ⅱ)型三角剖分△mn(2)下双周期二次样条空间S21(△mn...
In this method, we use the Crank-Nicolson scheme to discrete temporal variables and the cubic B-spline collocation method to discrete spatial variables. The method is stable and has second-order convergence for both time and space variables. The convergence analysis of the proposed method is ...
Type: Object Data: Two data vectors that define 1D function points Inputs: Name of first data column (e.g. x) Outputs: Name of second data column (e.g. y) Description: Cubic spline for nonlinear function approximation A cubic spline is a nonlinear function constructed of multiple third-...
–LinearB-splineshaveC0continuity,cubichaveC2,etc 4/29/04 ©UniversityofWisconsin,CS559Spring2004 UniformCubicB-splineon[0,1)•Fourcontrolpointsarerequiredtodefinethecurvefor0t<1(tistheparameter)–Notsurprisingforacubiccurvewith4degreesoffreedom •TheequationlooksjustlikeaBeziercurve,butwith...
Okay that is all the math you need to know to completely define the algorithm to compute a cubic spline. Here it is in Matlab: function [s0,s1,s2,s3]=cubic_spline(x,y) if any(size(x) ~= size(y)) || size(x,2) ~= 1 error('inputs x and y must be column vectors of equal...
we approximate the solution of fractional Painlevé and Bagley-Torvik equations in the Conformable (Co), Caputo (C), and Caputo-Fabrizio (CF) fractional derivatives using hybrid hyperbolic and cubic B-spline collocation methods, which is an extension of the third-degree B-spline function with more...