Remez algorithm: Difference between revisions

Revision as of 23:23, 3 November 2006

Revision as of 02:24, 4 November 2006

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The Remez algorithm starts with a set of sample points in the approximation interval, usually the [[Chebyshev nodes]] linearly mapped to the interval.

# A polynomial approximation of the function at the sample points is obtained through [[Lagrange polynomial|Lagrange interpolation]].

# The difference between the approximation and the function is measured across the interval. The point where the difference has the largest absolute value is found.

# The sample point nearest the ___location of the maximum absolute difference, is replaced with the ___location of the maximum absolute difference.

# The process is repeated until all sample points converge to the points of maximum absolute difference., Theand resultthe issign calledof the [[minimaxdifference approximation]]between the function and the polynomial alternates.

The result is called the polynomial of best approximation, the Chebyshev approximation, or the [[minimax approximation]].

==Variants==