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1.4 Newton Polynomial

This MATLAB function implements nested multiplication for constructing Newton's polynomial using given data points. The function `newpoly(X,Y)` takes in vectors X (nodal points) and Y (corresponding values) while calculating divided differences and coefficients. It initializes a matrix for divided differences, calculates through a nested loop, and constructs the polynomial using convolution for efficient evaluation. This approach is particularly useful in numerical analysis and interpolation tasks, ensuring high accuracy and simplicity in polynomial evaluation.

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1.4 Newton Polynomial

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  1. 1.4 Newton Polynomial

  2. 1.4.1 Nested Multiplication

  3. function [C,D]=newpoly(X,Y) n=length(X); D=zeros(n,n); D(:,1)=Y'; for j=2:n for k=j:n D(k,j)=(D(k,j-1)-D(k-1,j-1))/(X(k)-X(k-j+1)); end end C=D(n,n); for k=(n-1):-1:1 C=conv(C,poly(X(k))); m=length(C); C(m)=C(m)+D(k,k); end

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