Given n Points, find a Polynomial Function...Date: 6/27/96 at 22:36:47 From: Anonymous Subject: Given n Points, find a Polynomial Function... Dr. Math, I am having a problem with this question. Can you please help? Suppose (x1,y1),(x2,y2),...,(x(n),y(n)) are n points in the plane with the x(i)'s all different. Find a polynomial f1(x) of degree less than n so that f1(x1) = 1 and f1(x(j)) = 0 for all j not equal to 1 Find a polynomial F(x) of degree less than n so that the graph of F passes through all of the points (x1,y1),(x2,y2),..., (x(n),y(n)). Thank you. Richard Date: 6/28/96 at 13:36:23 From: Doctor Ceeks Subject: Re: Given n Points, find a Polynomial Function... Hi, Let pj(x) = (x-x1)(x-x2)...(x-x(n))/(x-xj). Let fj(x) = pj(x)/pj(xj). Then fj(xk) = 1 if j = k and 0 otherwise. Now let F = y1f1+y2f2+...+y(n)fn. These are standard constructions. -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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