HOW TO Generate Equation of a Curve Given (x,y) pairs - algorithm? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-20T03:14:42Z http://mathoverflow.net/feeds/question/54468 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/54468/how-to-generate-equation-of-a-curve-given-x-y-pairs-algorithm HOW TO Generate Equation of a Curve Given (x,y) pairs - algorithm? Murat 2011-02-05T22:09:17Z 2011-02-05T22:18:32Z <p>Hi,</p> <p>How can I generate the equation of a curve that matches all arbitrarily given (x,y) pairs? I would like a polynomial of nth degree, where n does not matter, as long as the curve passes thru all the given points.</p> <p>I guess this problem is NP-complete. If so, how do I find the closest matching curve in a feasible amount of time?</p> <p>Furthermore; how do I generate a piecewise polynomial, in case the given (x,y) pairs are discontinuous, or they draw the shape of a, say, circle?</p> <p>Thanks in advance.</p> http://mathoverflow.net/questions/54468/how-to-generate-equation-of-a-curve-given-x-y-pairs-algorithm/54469#54469 Answer by Dick Palais for HOW TO Generate Equation of a Curve Given (x,y) pairs - algorithm? Dick Palais 2011-02-05T22:18:32Z 2011-02-05T22:18:32Z <p>Actually, there is an easy and standard procedure (Lagrange Interpolation) that does this. See:</p> <p><a href="http://en.wikipedia.org/wiki/Lagrange_polynomial" rel="nofollow">http://en.wikipedia.org/wiki/Lagrange_polynomial</a></p>