1. Write an M-function function [x,iter,err]-Jacobi(A,b,tol,kmax) Then, test it for the solution of the linear system Ar= b with = to plit:([11 0 0 0 0]) and b chosen so that the exact solution of the system is z = [2.2.2.2.2.2]T. The output parameters are: x the solution vector; iter the number of iterations and err the relative errors among iterations. 2. Do the same for Gauss-Seidel 3. Again, with same data of the first exercise, write an M-function: function (x,iter,err]-SOR(A.b.tol.kmax,omega); that implements the relaxation method. Notice verify that this function can be used also as Gauss-Seidel method when omega=1 Without executing any code, verify if the Jacobi method couverges if the case when, given [1.1,5.2.2,5.3).we want to solve the system V'a = y, where = vander(r) and y= sin(x). The solution of the system, if exist, will give the coefficients of the interpolating polynomial of degre 4 of the sinus function at the equispaced points r.Which method, direct or iterative, could be applicable

1. Write an M-function function [x,iter,err]-Jacobi(A,b,tol,kmax) Then, test it for the solution of the linear system Ar= b with = to plit:([11 0 0 0 0]) and b chosen so that the exact solution of the system is z = [2.2.2.2.2.2]T. The output parameters are: x the solution vector; iter the number of iterations and err the relative errors among iterations. 2. Do the same for Gauss-Seidel 3. Again, with same data of the first exercise, write an M-function: function (x,iter,err]-SOR(A.b.tol.kmax,omega); that implements the relaxation method. Notice verify that this function can be used also as Gauss-Seidel method when omega=1 Without executing any code, verify if the Jacobi method couverges if the case when, given [1.1,5.2.2,5.3).we want to solve the system V'a = y, where = vander(r) and y= sin(x). The solution of the system, if exist, will give the coefficients of the interpolating polynomial of degre 4 of the sinus function at the equispaced points r.Which method, direct or iterative, could be applicable

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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Linear Programming Concepts

Linear programming is a famous mathematical modeling tool for determining the best distribution of scarce resources among competing demands. Machinery, time, personnel, raw materials, money, and space are all resources. It is used to find the most optimal solution to a problem with given constraints. The real-life situations can be formulated using linear programming concepts into a mathematical model. Linear programming problems consist of an objective function and linear equalities subjected to constraints.

Question

Solve the following problems in Octave or Matlab
1. Write an M-function
function [x,iter,err]-Jacobi(A,b,tol,kmax)
Then, test it for the solution of the linear system Ar= b with 1 toplit([11 0 0 0 0]) and b chosen so that
the exact solution of the system is z = [2.2.2.2.2.2]T. The output parameters are: x the solution vector; iter the
number of iterations and err the relative errors among iterations.
2. Do the same for Gauss-Seidel
3. Again, with same data of the first exercise, write an M-function: function (x,iter,err]-SOR(A.b.tol.kmax,omega);
that implements the relaxation method. Notice verify that this function can be used also as Gauss-Seidel method
when omega = 1
4. Without executing any code, verify if the Jacobi method couverges if the case when, given r = [1.1,5.2.2.5.3).we
want to solve the system V'a = y, where = vander(r) and y = sin(x). The solution of the system, if exist, will
give the coefficients of the interpolating polynomial of degre 1 of the sinus function at the equispared points r.Which
method, direct or iterative, could be applicable

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Step 1: 1. Jacobi Method Implementation:

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Step 2: 2. Gauss-Seidel Method Implementation:

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Step 3: 3. Successive Over-Relaxation (SOR) Method Implementation:

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Step 4: 4. Convergence of Jacobi Method:

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