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# hw8 - Homework 8 Foundations of Computational Math 2 Spring...

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Homework 8 Foundations of Computational Math 2 Spring 2011 Solutions will be posted Monday, 3/21/10 Problem 8.1 This is not a programming assignment and you need not turn in any code. This problem considers the used of discrete least squares for approximation by a polynomial. Recall, the distinct points x 0 < x 1 < ··· < x m are given and the metric m s i =0 ω i ( f ( x i ) p n ( x i )) 2 with ω i > 0 is used to determine the polynomial, p * n ( x ), of degree n that achieves the minimal value. We will assume ω i = 1 for this exercise. Typically, m n . If m = n then the unique interpolating polynomial is the solution. If we let p n ( x ) = n s j =0 φ j ( x ) γ j then the conditions are ρ 0 ρ 1 . . . ρ m = f ( x 0 ) f ( x 1 ) . . . f ( x m ) φ 0 ( x 0 ) . . . φ n ( x 0 ) φ 0 ( x 1 ) . . . φ n ( x 1 ) . . . . . . φ

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hw8 - Homework 8 Foundations of Computational Math 2 Spring...

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