In some numerical computing applications, a desired computation is to find a polynomial that goes through a
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In some numerical computing applications, a desired computation is to find a polynomial that goes through a given set of points on a line, which, without loss of generality, we can assume is the x-axis. So suppose you are given a set of real numbers
X = {x0, x1,...,xnā1}.
Note that, by the Interpolation Theorem for Polynomials, there is a unique degree- (n ā 1) polynomial p(x), such that
p(xi)=0, for i = 0, 1,...,n ā 1,
and these are the only 0-values for the polynomial. Design a divide-and-conquer algorithm that can construct a coefficient-form representation of this polynomial, p(x), using O(n log2 n) arithmetic operations.
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Related Book For
Algorithm Design And Applications
ISBN: 9781118335918
1st Edition
Authors: Michael T. Goodrich, Roberto Tamassia
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