 # Exercises 40—43 refer to another algorithm, known as Horner’s rule, for finding the value of a polynomial. Algorithm 11.3.4 Homer’s Rule [This algorithn computes the value of a polynomial a [ n ] x n + a [ n − 1 ] x n − 1 + ⋯ + a [ 2 ] x 2 + a [ 1 ] x + a [ 0 ] by nesting successive additions and multiplications as indicated in the following parenthesization: ( ( ⋯ ( ( a [ n ] x + a [ n − 1 ] ) x + a [ n − 2 ] ) x + ⋯ + a [ 2 ] ) x + a [ 1 ] ) x + a [ 0 ] . At each stage, starting with a [ n ] , the current value of polyval is multiplied by x and the next lower coefficient of the polynomial is added to it.] Input: n[a nonnegative integer], a [ 0 ] , a [ 1 ] , a [ 2 ] , … , a [ n ] [an array of real numbers], x [a real number] Algorithm Body: p o l y v a l : = a [ n ] for i : = 1 to n p o l y v a l : = p o l y v a l ⋅ x + a [ n − i ] next i [ A t t h i s p o i n t p o l y v a l = a [ n ] x n + a [ n − 1 ] x n − 1 + ⋯ + a [ 2 ] x 2 + a [ 1 ] x + a [ 0 ] . ] Output: polyval [a real number] 40. Trace Algorithm 11.3.4 for the input n = 3 , a [ 0 ] = 2 , a [ 1 ] = 1 , a [ 2 ] = − 1 , a [ 3 ] = 3 , and x = 2 . ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193 ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section
Chapter 11.3, Problem 40ES
Textbook Problem

## Expert Solution

### Want to see the full answer?

Check out a sample textbook solution.See solution

### Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

See Solution

*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects. 