Lagrange Interpolation for 4th order

Richard Flores

2019 4 8

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function ya = Lagrange(x,y,a)

n_x = length(x);

n_y = length(y);

if n_x ~= n_y

error('The size of the x and y vectors are not compatible')

end

y1_num = (y(1,1) .* (a-x(2,1)).*(a-x(3,1)).*(a-x(4,1)).*(a-x(5,1)));

y2_num = (y(2,1) .* (a-x(1,1)).*(a-x(3,1)).*(a-x(4,1)).*(a-x(5,1)));

y3_num = (y(3,1) .* (a-x(1,1)).*(a-x(2,1)).*(a-x(4,1)).*(a-x(5,1)));

y4_num = (y(4,1) .* (a-x(1,1)).*(a-x(2,1)).*(a-x(3,1)).*(a-x(5,1)));

y5_num = (y(5,1) .* (a-x(1,1)).*(a-x(2,1)).*(a-x(3,1)).*(a-x(4,1)));

y1_denom =((x(1,1)- x(2,1)).*(x(1,1)-x(3,1)).*(x(1,1)-x(4,1)).*(x(1,1)-x(5,1)));

y2_denom =((x(2,1)- x(1,1)).*(x(2,1)-x(3,1)).*(x(2,1)-x(4,1)).*(x(2,1)-x(5,1)));

y3_denom =((x(3,1)- x(1,1)).*(x(3,1)-x(2,1)).*(x(3,1)-x(4,1)).*(x(3,1)-x(5,1)));

y4_denom =((x(4,1)- x(1,1)).*(x(4,1)-x(2,1)).*(x(4,1)-x(3,1)).*(x(4,1)-x(5,1)));

y5_denom =((x(5,1)- x(1,1)).*(x(5,1)-x(2,1)).*(x(5,1)-x(3,1)).*(x(5,1)-x(4,1)));

y1 = y1_num./y1_denom;

y2 = y2_num./y2_denom;

y3 = y3_num./y3_denom;

y4 = y4_num./y4_denom;

y5 = y5_num./y5_denom;

ya = y1 + y2 + y3 + y4 + y5;

end

I am trying to run a code for 5 data points and evaluate the given equation at a specific value. I can not figure out how to input the value of "a" from the command window where I am also inputting the arrays (which are both 5X1). And when I do assign a value for a and check the answer with a lagrange calculator online, the y value is wrong. Any help would be appreciated.