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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), z). 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 p₁ (x) is subtracted from p₂(x). 4. Multiply(p, (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: f(x₂-₁) k=1,2,... Start with the initial approximation xo = 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 Xo 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), z). 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 p₁ (x) is subtracted from p₂(x). 4. Multiply(p, (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: f(x₂-₁) k=1,2,... Start with the initial approximation xo = 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 Xo 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

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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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), z). 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 p₁ (x) is subtracted from p₂ (x). 4. Multiply(p, (x), p₂(x)). Returns the polynomial that results when p, (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: f(x₂-₁) f'(xx-₁)' 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 to 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: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), z). 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 p₁ (x) is subtracted from p₂ (x). 4. Multiply(p, (x), p₂(x)). Returns the polynomial that results when p, (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: f(x₂-₁) f'(xx-₁)' 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 to 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
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