3.3 5x - 2y + z = 4 7x + y - 5z = 8 3x + 7y + 4z = 10) by using LU-Factorization Method.
3.3 5x - 2y + z = 4 7x + y - 5z = 8 3x + 7y + 4z = 10) by using LU-Factorization Method.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
Related questions
Question
![3.3
5x - 2y + z = 4
7x + y - 5z = 8
3x + 7y + 4z = 10)
x + 5y + z = 14
3.4 2xy + 8z = 12
4x + y + 3z = 17
4aß +y = 8)
4α
by using LU-Factorization Method.
by Gauss Jacobi Iterative Method up to four iterations
(Starting with x(0) = 1, y = 1, z0) = 1)
3.5 2a +58 +2y = 3 by Gauss-Seidel iterative technique up to three iterations
a + 2B + 4y = 11)
4. Answer the following Questions and Calculate Relative Error and Percentage Error in
each case:
4.1 Use the Bisection Method to find a solution of the equation 3x - e* = 0 on the
interval [1,2] with an accuracy of 10-³.
4.2 Use the Newton-Raphson Method to find a solution accurate to within 10-6 for the
following equation: sin x = ex, for 0≤x≤1
4.3 Use the Second Method to find an approximation to (29)1/4, accurate to within
10-4.
5. Use Newton-Iterative Techniques to find approximate solutions up to 2nd iterations to
the given nonlinear system of equations. Choose: (xo, Yo) = (3,2)
x² - y² = 4
x² + y² = 16](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5afe2ef8-0c98-40df-91df-c1dde9e674bb%2F2a41a0f8-1b50-4c2a-95df-3326cd24390f%2Fmr0tewr_processed.png&w=3840&q=75)
Transcribed Image Text:3.3
5x - 2y + z = 4
7x + y - 5z = 8
3x + 7y + 4z = 10)
x + 5y + z = 14
3.4 2xy + 8z = 12
4x + y + 3z = 17
4aß +y = 8)
4α
by using LU-Factorization Method.
by Gauss Jacobi Iterative Method up to four iterations
(Starting with x(0) = 1, y = 1, z0) = 1)
3.5 2a +58 +2y = 3 by Gauss-Seidel iterative technique up to three iterations
a + 2B + 4y = 11)
4. Answer the following Questions and Calculate Relative Error and Percentage Error in
each case:
4.1 Use the Bisection Method to find a solution of the equation 3x - e* = 0 on the
interval [1,2] with an accuracy of 10-³.
4.2 Use the Newton-Raphson Method to find a solution accurate to within 10-6 for the
following equation: sin x = ex, for 0≤x≤1
4.3 Use the Second Method to find an approximation to (29)1/4, accurate to within
10-4.
5. Use Newton-Iterative Techniques to find approximate solutions up to 2nd iterations to
the given nonlinear system of equations. Choose: (xo, Yo) = (3,2)
x² - y² = 4
x² + y² = 16
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