Question
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The Hilbert matrices H arise in finding polynomial approximations to functions defined on the unit interval. For example, when approximating the function sin(pix) on [0,1] , the coefficients of the polynomial p(x) of degree n-1 that minimizes the squared error are solutions of the matrix equation Using the following techniques explore the believer of the solutions to (1) for values of n up to 25: using basic Gaussian elimination using Gaussian elimination with (partially) scaled partial pivoting using LU factorization using Gauss - Seidel iteration in each case compute the residual error vector r = b - compare vour results for the three methods.
Explanation / Answer
raise the points,,,,
or...
get take as much help as we give :p
visit these
http://mathoverflow.net/questions/124161/hilbert-matrix-and-approximation-theory
eprints.maths.ox.ac.uk/938/1/NA-10-05.pdf?