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NUMERICAL ANALYSIS
MATLAB-3: linear system::: matlab code needed
Write a MATLAB program to implement the
Test your implementation to solve the following system of linear equations:
x + 2y - 2z +w = 0
2x +5y + z + w = 13
x + y + 4z +w = 10
3x -y -z + 6w = -7
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- Write computer codes using any programming language for one of the following methods to solve a linear equation system.1- Gaussian elimination.2- LU decomposition.3- Gauss-Seidel iterations.Execute the program for the linear equation system given below.NUMERICAL ANALYSIS::::::: Write a MATLAB program for the Newton-Raphson method. Write your name, ID, and number of the Section inside the code. Test your algorithm to find the root of the function: f(x) = cos(x) + 1/(1+x^2) defined on the interval [0.4, 4.5]. The angles are in radian. Start with the initial value for x to be 1.2. Stop the running until 10 iterations or relative approximated error is less than 0.05. Display the output for each iteration.using Matlab Write a program that solves a quadratic equation using the constitutional method Quadratic equation (Function M-file) (-b+ vb2 - 4ac b2 – 4ac > 0 2a -b b2 – 4ac = 0 2a If the value under the root is less than zero, print the expression (the root is complex)
- Find the root of tg(x)=1/2which is between x=0.6 and x=0.7. Use Newton Raphson's method (if it is possible to make a code in matlab)and start calculations with x=0.6.Thanks in advanceTROUBLESHOOTING: Fix the errors in the code below MATLAB function [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % Solves Ax = b by Gauss-Seidel method with relaxation. % USAGE: [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % INPUT: % func = handle of function that returns improved x using % x = starting solution vector % maxIter = allowable number of iterations (default is 500) % epsilon = error tolerance (default is 1.0e-9) % OUTPUT: % x = solution vector % numIter = number of iterations carried out % omega = computed relaxation factor if nargin < 4; epsilon = 1.0e-9; end if nargin < 3; maxIter = 500; end k = 10; p = 1; omega = 1; for numIter = 1:maxIter xOld = x; x = feval(func,x,omega); dx = sqrt(dot(x - xOld,x - xOld)); if dx < epsilon; return; end if numIter == k; dx1 = dx; end if numIter == k + p omega = 2/(1 + sqrt(1 - (dx/dx1)ˆ(1/p))); end end error(’Too many iterations’)create a recursive equation for function max(a,b) where a if a<b, b otherwise
- Python application creation The system call inv in the numpy.linalg library can be used to calculate the inverse of a matrix. A basic 2 by 2 matrix's inverse can be calculated using Python code. The identity matrix I is then generated by multiplying the inverse of A by itself for proof.Write computer program to solve a set of equation by using Gauss-Seidel Iteration.Using a for-loop in Matlab for the given vectors V=[17,9, 3, 6, 10]; W=[9, 6, 7,7, 1]; a) Write a program (using for-loop) that calculates the dot-product, C=(V-W).W b) What is the value of C? Choices 280 63 68 64 Submit I Attempts 1 |
- Explain the Solutions of Optimization Problems with a Random Structure?PYTHON /JUPYTER NOTEBOOKS Program a backward solver (i.e. write your code) for an upper triangular system Ux=b. The algorithm is attached below for Numpy and Python with offset 1. Recall that NumPy and Python have offset 0 for their sequence data types.For the given tabulating problem, solve for the needed: Note: This problem was quoted from: An Introduction to Matlab David F. Gri_ths formerly of Department of Mathematics, The University of Dundee, Dundee DD1 4HN Scotland, UK Exercise 14.1 Tabulate the functions y = (x² + 3) sin x² and -2 z=sin? næ/(z~2+3) for x = 0,0.2,..., 10. Hence, tabulate the func- tion (x²+3) sin Tx² sin² Tx (x−²+3) Plot a graph of w over the range 0≤ x ≤ 10. W= - Write a computer algorithm (with python) for tabulating the resulting numbers.