MATLAB: Alternates of polyval and polyfit

polyfitpolyval

I'm working on an assignment that has to do with interpolating polynomials where I create a picture reading in the data points from a file. However, I am not allowed to use the functions polyfit or polyval. How would I go about finding the coefficients of a polynomial and generating a curve based on those coefficients?

Best Answer

https://en.wikipedia.org/wiki/Vandermonde_matrix

Suppose you had a polynomial of degree 2, y = a2*x^2 + a1*x^1 + a0*x^0, a2, a1, a0 unknown then you can write that as

[x^2, x^1, x^0] * [a2; a1; a0] = y

Now fill in those values as columns for all known x, y

A = [x1^2, x1, 1
     x2^2, x2, 1
     x3^2, x3, 1
     ...]
b = [y1;
     y2
     y3
     ...]

and then it follows that

  A * [a2; a1; a0] = b

which is a (possibly overdetermined) system of simultaneous linear equations you can solve by your favorite method

Related Solutions

MATLAB: Create a vector form a polynomial evaluation

y = cellfun(@(x,y)polyval(x,y),num2cell(M,2),num2cell(X));

y = arrayfun(@(n)polyval(M(n,:),X(n)),(1:numel(X))');

MATLAB: Polyfit, polyval and plot

Because the syntax should be

polyfit(x,y,N)

and not

polyfit(y,x,N)

Here is some code that illustrates the fix:

x = 1:503;

y = 250 + 0.02*x + 0.005*x.^2 + 0.2*rand(1,503).*x;

figure
polyfit(y,x,0);
coef1 = polyfit(x,y,0);
y1 = polyval(coef1,x);
hold on
plot(x,y,'.');
plot(x,y1);  
polyfit(x,y,1);
coef2 = polyfit(x,y,1);
y2 = polyval(coef2,x);
plot(x,y2);
polyfit(y,x,2);
coef3 = polyfit(x,y,2);
y3 = polyval(coef3,x);
plot(x,y3);

Best Answer

Related Solutions

MATLAB: Create a vector form a polynomial evaluation

MATLAB: Polyfit, polyval and plot

Related Question