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(a) -The naive algorithm computes independently each of the terms aixo, a₂x, a3x,...,anx and then adds all of these numbers to ao to obtain p(xo). How many sums and how many multiplications are used by this algorithm, as a function of n? (You can give your answer in O-notation.)

(a) -The naive algorithm computes independently each of the terms aixo, a₂x, a3x,...,anx and then adds all of these numbers to ao to obtain p(xo). How many sums and how many multiplications are used by this algorithm, as a function of n? (You can give your answer in O-notation.)

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter2: Basic Linear Algebra
Section: Chapter Questions
Problem 15RP
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Evaluating Polynomials Consider a polynomial given by p(x) = ao+a₁x+a₂x² + ... + a₂x². Consider the problem of evaluating it at some point xo, i.e. computing p(xo).
Transcribed Image Text:Evaluating Polynomials Consider a polynomial given by p(x) = ao+a₁x+a₂x² + ... + a₂x². Consider the problem of evaluating it at some point xo, i.e. computing p(xo).
(a) The naive algorithm computes independently each of the terms aixo, a2x, a3x,...,anx and then adds all of these numbers to ao to obtain p(xo). How many sums and how many multiplications are used by this algorithm, as a function of n? (You can give your answer in O-notation.)
Transcribed Image Text:(a) The naive algorithm computes independently each of the terms aixo, a2x, a3x,...,anx and then adds all of these numbers to ao to obtain p(xo). How many sums and how many multiplications are used by this algorithm, as a function of n? (You can give your answer in O-notation.)
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