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Develop a program that implements the POLYNOMIAL ADT using the LIST ADT. e POLYNOMIAL ADT is used to represent polynomials and the following operations fined on polynomials: 1. Evaluate(p(x), =). Evaluates the polynomial p(x) at the point x = z and returns the result. 2. Add(P₁(x), P₂(x)). Returns the polynomial that results when p, (x) is added to P₂(x). 3. Subtract(p, (x), p₂(x)). Returns the polynomial that results when p, (x) is subtracted from p₂(x). 4. Multiply(p, (x), p₂(x)). Returns the polynomial that results when p₁(x) is multiplied by n. (x)

Develop a program that implements the POLYNOMIAL ADT using the LIST ADT. e POLYNOMIAL ADT is used to represent polynomials and the following operations fined on polynomials: 1. Evaluate(p(x), =). Evaluates the polynomial p(x) at the point x = z and returns the result. 2. Add(P₁(x), P₂(x)). Returns the polynomial that results when p, (x) is added to P₂(x). 3. Subtract(p, (x), p₂(x)). Returns the polynomial that results when p, (x) is subtracted from p₂(x). 4. Multiply(p, (x), p₂(x)). Returns the polynomial that results when p₁(x) is multiplied by n. (x)

Database System Concepts
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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Program in C
on nction is defined as follows: X = X-1 f(x) f'(x) k = 1,2,... Start with the initial approximation x = 3. (1) If f(x), f (x), and f(x) are continuous near the root r, and f (r) = 0, then if the initial approximation is chosen close enough to r, the sequence {x} defined in (1) will converge to r. Test your Newton-Raphson program on the polynomial p(x) = x² - 6x +8x³+8x² + 4x − 4
Transcribed Image Text:on nction is defined as follows: X = X-1 f(x) f'(x) k = 1,2,... Start with the initial approximation x = 3. (1) If f(x), f (x), and f(x) are continuous near the root r, and f (r) = 0, then if the initial approximation is chosen close enough to r, the sequence {x} defined in (1) will converge to r. Test your Newton-Raphson program on the polynomial p(x) = x² - 6x +8x³+8x² + 4x − 4
Develop a program that implements the POLYNOMIAL ADT using the LIST ADT. The POLYNOMIAL ADT is used to represent polynomials and the following operations defined on polynomials: 1. Evaluate(p(x), =). Evaluates the polynomial p(x) at the point x = z and returns the result. 2. Add(P₁(x), P₂(x)). Returns the polynomial that results when p₁(x) is added to P₂ (x). 3. Subtract(p, (x), p₂(x)). Returns the polynomial that results when p, (x) is subtracted from p₂(x). 4. Multiply(p₁(x), p₂(x)). Returns the polynomial that results when p₁(x) is multiplied by p₂(x). 5. Differentiate( p(x)). Returns the polynomial that results when p(x) is differentiated. Use your POLYNOMIAL ADT implementation to find a real root of a given polynomial using the Newton-Raphson method. For a given function f(x), the Newton- Raphson iteration function is defined as follows: X = X-1 f(xx-1) f'(xx-1)' k = 1,2,... (1) If f(x), f'(x), and f(x) are continuous near the root r, and f'(r) = 0, then if the initial approximation to is chosen close enough to r, the sequence {x} defined in (1)
Transcribed Image Text:Develop a program that implements the POLYNOMIAL ADT using the LIST ADT. The POLYNOMIAL ADT is used to represent polynomials and the following operations defined on polynomials: 1. Evaluate(p(x), =). Evaluates the polynomial p(x) at the point x = z and returns the result. 2. Add(P₁(x), P₂(x)). Returns the polynomial that results when p₁(x) is added to P₂ (x). 3. Subtract(p, (x), p₂(x)). Returns the polynomial that results when p, (x) is subtracted from p₂(x). 4. Multiply(p₁(x), p₂(x)). Returns the polynomial that results when p₁(x) is multiplied by p₂(x). 5. Differentiate( p(x)). Returns the polynomial that results when p(x) is differentiated. Use your POLYNOMIAL ADT implementation to find a real root of a given polynomial using the Newton-Raphson method. For a given function f(x), the Newton- Raphson iteration function is defined as follows: X = X-1 f(xx-1) f'(xx-1)' k = 1,2,... (1) If f(x), f'(x), and f(x) are continuous near the root r, and f'(r) = 0, then if the initial approximation to is chosen close enough to r, the sequence {x} defined in (1)
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