There is a more efficient algorithm (in terms of the Problem 14E Chapter 3.3

Discrete Mathematics and Its Applications | 7th Edition

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Problem 14E

There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials than the conventional algorithm described in the previous exercise. It is called Horner's method. This pseudocode shows how to use this method to find the value of anxn + an-1xn-1+ … +a1x + a0 at x = c

procedure Honer(c, a0. a1 ,…, an: real numbers)

y := an

for i := 1 to n

y := y * c + an−1

return y {y = ancn + an−1cn−1 + … + a1c + a0}

a)     Evaluate 3x2 + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step.

b)    Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)

Step-by-Step Solution:

Solution:Step 1</p>

In this problem we need to find the value of polynomial at using the given algorithm.

Given algorithm :

procedure Honer( real numbers)

y := for i := 1 to n

y := return y { }

where the final value of y is the value of the polynomial at x = c.

Step 2</p>

To find the value of the polynomial at using algorithm we do as follows.

Initial conditions of the algorithm are : and Step 1 of the algorithm:

For we have and y := y := y :=  Therefore for , and Step 2 of the algorithm:

For we have and y := y := y :=  Therefore for , and Thus the value of the polynomial at is 15 by using the algorithm.

Step 2 of 2

ISBN: 9780073383095

This full solution covers the following key subjects: multiplications, Algorithm, additions, used, method. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Since the solution to 14E from 3.3 chapter was answered, more than 278 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th. The answer to “There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials than the conventional algorithm described in the previous exercise. It is called Horner's method. This pseudocode shows how to use this method to find the value of anxn + an-1xn-1+ … +a1x + a0 at x = cprocedure Honer(c, a0. a1 ,…, an: real numbers)y := anfor i := 1 to ny := y * c + an?1return y {y = ancn + an?1cn?1 + … + a1c + a0}a) Evaluate 3x2 + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step.________________b) Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)” is broken down into a number of easy to follow steps, and 147 words. The full step-by-step solution to problem: 14E from chapter: 3.3 was answered by , our top Math solution expert on 06/21/17, 07:45AM.

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