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 anx" + An-1x²-¹ +...+ a₁x + ao = 0 at x = c. procedure Horner(c, ao, a₁, a2,..., an: real numbers) y := an for i:=1 to n y := y*c+an-i return y(y = anc" +an-1-1+...+ a₁c + ao} 2.a Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. 2.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.)

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 anx" + An-1x²-¹ +...+ a₁x + ao = 0 at x = c. procedure Horner(c, ao, a₁, a2,..., an: real numbers) y := an for i:=1 to n y := y*c+an-i return y(y = anc" +an-1-1+...+ a₁c + ao} 2.a Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. 2.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.)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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