I was reading John Randall's wiki entry http://www.jsoftware.com/jwiki/JohnRandall/FourierTransformAndPolynomialMultiplication and I got stuck on the third paragraph where he mentions Lagrange interpolation. I have some half remembered concepts which might be relevant, but that does not mean that I understand what he wrote.
So, I was working through a wikipedia page on the subject http://en.wikipedia.org/wiki/Lagrange_polynomial and, again, I got stuck. This time on their definition of lagrange polynomials. First, let me define a polynomial in terms of coefficients of powers of x: c=: 720%!i.7 Now, for the lagrange approach, I need to pick some distinct values for x X=: i.#c and, I need the corresponding Y values Y=: c p. X Now, according to the definition on that wikipedia page, a lagrange basis polynomial verb would look something like this: l=: - */@(-.&__ 0 _)@:%"1 -/[EMAIL PROTECTED] 3.5 l X _0.00488281 0.0410156 _0.170898 0.683594 0.512695 _0.0683594 0.00683594 And, the corresponding lagrange polynomial would look like this: L=: ({:@] +/ .* [ l [EMAIL PROTECTED])"0 2 3.5 L X,:Y 22286.5 But I have something wrong, because: Y-: X L X,:Y 0 And when I examine another page describing these polynomials, like http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html I see basically the same definition as was presented in the wikipedia, so I do not think my problem is in the definition. Can anyone help me identify where I went wrong? I would especially appreciate any advice on systematic approaches to finding this kind of error, but any corrections would be great. Thanks, -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
