Scilab/C4/Linear-equations-Iterative-Methods/English - Revision history

Nancyvarkey at 16:51, 1 February 2014

2014-02-01T16:51:18Z

Nancyvarkey at 13:56, 27 December 2013

2013-12-27T13:56:05Z

Lavitha Pereira: Created page with ''''Title of script''': Solving System of Linear Equations using Iterative Methods '''Author: Shamika''' '''Keywords: System of linear equations, Iterative Methods''' {| styl…'

2013-12-18T05:02:21Z

Created page with ''''Title of script''': Solving System of Linear Equations using Iterative Methods '''Author: Shamika''' '''Keywords: System of linear equations, Iterative Methods''' {| styl…'

New page

'''Title of script''': Solving System of Linear Equations using Iterative Methods

'''Author: Shamika'''

'''Keywords: System of linear equations, Iterative Methods'''

{| style="border-spacing:0;"
! <center>Visual Cue</center>
! <center>Narration</center>

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 1
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Dear Friends,

Welcome to the Spoken Tutorial on “'''Solving System of Linear Equations using Iterative Methods'''”

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 2 -Learning Objective Slide
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| At the end of this tutorial, you will learn how to:

* Solve system of linear equations using iterative methods
* Develop Scilab code to solve linear equations

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 3-System Requirement slide
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| To record this tutorial, I am using '''Ubuntu 12.04''' as the operating system with '''Scilab 5.3.3''' version

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 4- Prerequisites slide
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Before practising this tutorial, a learner should have basic knowledge of '''Scilab and Solving Linear Equations'''

For Scilab, please refer to the relevant tutorials available on the '''Spoken Tutorial '''website.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 5- Jacobi Method
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The first iterative method we will be studying is '''Jacobi method.'''
* Given a '''system of linear equations, with n equations and n unknowns'''
* We rewrite the equations such tha'''t x of i k plus one is equal to b i minus summation of a i j x j k from j equal to one to n divided by a i i where i is from one to n'''
* We assume values for each''' x of i'''
* Then we substitute the values in the equations obtained in the previous step.
* We continue the iteration until the solution converges.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 6- Example
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us solve this example using '''Jacobi Method'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to Scilab and open JacobiIteration_final.sci
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us look at the code for '''Jacobi Method'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''format('e',20)'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We use '''format''' method to specify the format of the displayed answers on the Scilab console.
* Here '''e '''denotes the answer should be in '''scientific notation''' and '''twenty''' specifies the number of digits to be displayed.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''A=input("Enter the coeffiecient matrix of nxn: ")'''

'''b=input("Enter the right-hand side matrix nx1: ")'''

'''x0=input("Initial approximation nx1: ")'''

'''MaxIter=input("Maximum no. of iterations: ")'''

'''tol=input("Enter the convergence tolerance :")//stop if norm <nowiki>change in x < tol</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Then we use '''input''' function to get the values for the '''matrices coefficient matrix, right hand side matrix, initial values matrix, maximum number of iteration and convergence tolerance'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''<nowiki>[m, n] = size( A )</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Then we use''' size '''function to check if '''A matrix is a square matrix.'''
* If it isn't, we use '''error function''' to display an error

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''for i=1:1:m'''

'''sum=0;'''

'''for j=1:1:m'''

'''sum=sum+abs(A(i,j));'''

'''end'''

'''<nowiki>if 2*abs(A(i,i))<sum then</nowiki>'''

'''error("the matrix is not diagonally dominant")'''

'''end'''

'''end'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We then check if matrix A is '''diagonally dominant'''.
* The first half calculates the sum of each row of the matrix.
* Then it checks if the twice the product of the diagonal element is greater than the sum of the elements of that row.
* If it isn't, an error is displayed using '''error function'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''<nowiki>function [ solution ] = JacobiIteration( A, b, x0, MaxIter, tol )</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Then we define the function '''Jacobi Iteration''' with input arguments '''A, b , x zero, maximum iteration and tolerance level'''.
* Here '''x zero''' is the '''initial values matrix'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''if ( length(x0) ~= n )'''

'''error( "Sizes of input matrix and input vector do not match" )'''

'''end'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We check if the size of A matrix and initial values matrix are compatible with each other.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''xk = x0'''

'''for k = 1 : 1 : MaxIter'''

'''for i = 1 : n'''

'''xkp1( i ) = (b(i) - A(i, 1:i-1)*xk(1:i-1) - A(i, i+1:n)*xk(i+1:n)) / A(i,i) //Computes the jacobian updates'''

'''end'''

'''RelativeError = norm( xkp1 - xk, 'inf' ) / norm( xkp1, 'inf' )'''

'''printf( "iter = %d, Relative Error = %g\n", k, RelativeError )'''

'''xk = xkp1'''

'''<nowiki>if ( RelativeError < tol )</nowiki>'''

'''break'''

'''end'''

'''end'''

'''solution = xkp1'''

'''endfunction'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We calculate the value for''' x k p one''' and then check if the '''relative error is lesser than tolerance level.'''
* If it is lesser than '''tolerance level''', we break the iteration and the solution is returned.
* Finally we '''end the function'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Click on Execute and select Save and Execute
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us '''save and execute the function'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to Scilab console
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Switch to '''Scilab console'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Enter these values on Scilab console for each prompt

Enter the coeffiecient matrix of nxn: '''<nowiki>[2 1;5 7]</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us enter the values at each prompt.

* The '''coefficient matrix A is '''
* '''open square bracket two space one '''
* '''semi colon '''
* '''five space seven close square bracket'''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type

Enter the right-hand side matrix nx1: '''<nowiki>[11; 13]</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Then we type
* '''open square bracket eleven '''
* '''semicolon '''
* '''thirteen'''
* '''press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type

Initial approximation nx1: '''<nowiki>[1;1]</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The initial values matrix is
* '''open square bracket one '''
* '''semi colon '''
* '''one close square bracket'''
* '''press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type

Maximum no. of iterations: '''25'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The maximum number of iterations is''' twenty five'''
* '''press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type

Enter the convergence tolerance :'''0.00001'''

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let the convergence tolerance level be''' zero point zero zero zero zero one'''
* '''press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type:

'''JacobiIteration( A, b, x0, MaxIter, tol )'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We call the function by typing '''Jacobi Iteration open paranthesis A comma b comma x zero comma M a x I t e r comma t o l close paranthesis'''
* '''Press Enter'''
* The values for '''x one''' and '''x two''' are shown on the console.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 7- Gauss Seidel Method
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us now study Gauss Seidel method.
* Given a '''system of linear equations, with n equations and n unknows'''
* We rewrite the equations for each unknown, '''by subtracting the other variables and their coefficients from the corresponding right hand side element.'''
* Then we divide this '''by the coefficient a i i of the unknown variable for that variable'''.
* This is done for every given equation.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 8- Gauss Seidel
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * In '''Jacobi method''', for '''the computation of x of i k plus one, every element of x of i k is used except x of i k plus one'''
* In '''Gauss Seidel method''', we '''over write the value of x of i k with x of i k plus one'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 9- Example
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us solve this example using '''Gauss Seidel Method'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to Scilab editor and open GaussSeidel.sci

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us look at the code for '''Gauss Seidel Method'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''format('e',20)'''

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The first line specifies the format of the displayed answer on the console using '''format function'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''A=input("Enter the coeffiecient matrix of nxn: ")'''

'''b=input("Enter the right-hand side matrix nx1: ")'''

'''x0=input("Initial approximation nx1: ")'''

'''MaxIter=input("Maximum no. of iterations: ")'''

'''tol=input("Enter the convergence <nowiki>tolerance :")//stop if norm change in x < tol</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Then we use '''input function''' to get the values of '''coefficient matrix, right hand side matrix, initial values of the variables matrix, maximum number of iteration and tolerance level'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''<nowiki>function [ solution ] = GaussSeidel( A, b, x0, MaxIter, tol )</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Then we define the function '''Gauss Seidel '''with''' input arguments A comma b comma x zero comma Max Iterations '''and '''tolerance level''' and output argument solution

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''// Check that the matrix is square'''

'''<nowiki>[m, n] = size( A )</nowiki>'''

'''if ( m ~= n )'''

'''error( "The input matrix is not square" )'''

'''end'''

'''// Check that the initial vector is of the same size'''

'''if ( length(x0) ~= n )'''

'''error( "Sizes of input matrix and input vector do not match" )'''

'''end'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We check if '''matrix A is square''' and the sizes of '''initial vector and matrix A''' are compatible using''' size and length function'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

'''xk = x0'''

'''xkp1 = zeros( xk )'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Then we start the iterations. We equate the '''initial values vector x zero to x k.'''
* We create a '''matrix of zeros with the same size of x k and call it x k p one.'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Highlight

for k = 1 : 1 : MaxIter

'''// Computes the Gauss-Seidel update'''

'''for i = 1 : n'''

'''xkp1( i ) = (b(i) - A(i, 1:i-1)*xkp1(1:i-1) - A(i,i+1:n)*xk(i+1:n)) / A(i,i)'''

'''// x^{k+1}'''

'''end'''

'''// Applies the relaxation'''

'''RelativeError = norm( xkp1 - xk, 'inf' ) / norm( xkp1, 'inf' )'''

'''printf( "iter = %d, Relative Error = %g\n", k, RelativeError )'''

'''xk = xkp1'''

'''<nowiki>if ( RelativeError < tol )</nowiki>'''

'''break'''

'''end'''

'''end'''

'''solution = xkp1'''

'''endfunction'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We solve for each equation to get the value of the unknown variable for that equation using '''x k p one'''.
* At each iteration, the value of '''x k p one''' gets updated.
* Also, we check if '''relative error is lesser than specified tolerance level'''.
* If it is, we '''break the iteration'''.
* Then '''equate x k p one to the variable solution'''.
* Finally, we '''end the function'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Click on Execute and select Save and Execute
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us '''save and execute the function'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to Scilab console
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Switch to '''Scilab console'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type the following on Scilab console:

For first prompt

'''<nowiki>[2 1;5 7]</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * For the first prompt we type '''matrix A.'''

* Type
* '''open square bracket two space one '''
* '''semi colon '''
* '''five space seven close square bracket'''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Second prompt

'''<nowiki>[11; 13]</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * For the next prompt, type
* '''left square bracket eleven'''
* '''semi colon'''
* '''thirteen right square bracket'''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| For third prompt

'''<nowiki>[1;1]</nowiki>'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We provide the values of '''initial value vector '''by typing
* '''open square bracket one '''
* '''semicolon '''
* '''one close square bracket'''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| For fourth prompt

'''25'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Then we specify the''' maximum number of iterations to be twenty five'''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| For fifth prompt

'''0.00001'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us define tolerance level to be''' zero point zero zero zero zero one'''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Then type:

'''GaussSeidel( A, b, x0, MaxIter, tol )'''

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Finally we call the function by typing''' G a u s s S e i d e l open paranthesis A comma b comma x zero comma M a x I t e r comma t o l close paranthesis'''
* '''Press enter'''
* The values of '''x one and x two '''are displayed.
* The number of iterations to solve the same problem are lesser than '''Jacobi method'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 13- Solve
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Solve this problem on your own using '''Jacobi and Gauss Seidel '''methods

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 14- Summary
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| In this tutorial, we have learnt to:

* Develop '''Scilab code''' for solving system of linear equations
* Find the value of the unknown variables of a system of linear equations

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide 15'''

'''Title: About the Spoken Tutorial Project'''

* Watch the video available at [http://spoken-tutorial.org/What_is_a_Spoken_Tutorial http://spoken-][http://spoken-tutorial.org/What_is_a_Spoken_Tutorial tutorial.org/What_is_a_Spoken_Tutorial]

* It summarises the Spoken Tutorial project

* If you do not have good bandwidth, you can download and watch it

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * About the Spoken Tutorial Project

* Watch the video available at the following link

* It summarises the Spoken Tutorial project

* If you do not have good bandwidth, you can download and watch it

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide 16'''

'''Title: Spoken Tutorial Workshops'''

The Spoken Tutorial Project Team

* Conducts workshops using spoken tutorials

* Gives certificates for those who pass an online test

* For more details, please write to contact@spoken-tutorial.org

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The Spoken Tutorial Project Team

* Conducts workshops using spoken tutorials

* Gives certificates for those who pass an online test

* For more details, please write to contact at spoken hyphen tutorial dot org

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide 17'''

'''Title: Acknowledgement'''

* Spoken Tutorial Project is a part of the Talk to a Teacher project

* It is supported by the National Mission on Education through ICT, MHRD, Government of India

* More information on this Mission is available at

* [http://spoken-tutorial.org/NMEICT-Intro http://spoken-tutorial.org/NMEICT-][http://spoken-tutorial.org/NMEICT-Intro Intro]

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Spoken Tutorial Project is a part of the Talk to a Teacher project
* It is supported by the National Mission on Education through ICT, MHRD, Government of India
* More information on this Mission is available at
* spoken hyphen tutorial dot org slash NMEICT hyphen Intro

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"|
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * This is Ashwini Patil signing off. Thank you for joining.

|}

@@ Line 61: / Line 61: @@
-Here '''e '''denotes the answer should be in '''scientific notation''' and twenty specifies the number of digits to be displayed.
+Here '''e '''denotes the answer should be in '''scientific notation'''.
 |-
@@ Line 86: / Line 88: @@
 '''<nowiki>[m, n] = size( A )</nowiki>'''
-| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"|Then we use''' size '''function to check if '''A matrix is a square matrix.'''
+| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"|Then we use''' size '''function to check if '''A matrix''' is a '''square matrix.'''
@@ Line 114: / Line 116: @@
 * We then check if '''matrix A''' is '''diagonally dominant'''.
 * The first half calculates the sum of each row of the '''matrix'''.
-* Then it checks if twice the product of the diagonal element is greater than the sum of the elements of that row.
+* Then it checks if twice the product of the '''diagonal element''' is greater than the sum of the elements of that row.
 * If it isn't, an error is displayed using '''error function'''.
@@ Line 121: / Line 123: @@
 '''<nowiki>function [ solution ] = JacobiIteration( A, b, x0, MaxIter, tol )</nowiki>'''
-| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"|Then we define the function '''Jacobi Iteration''' with input arguments '''A, b , x zero, maximum iteration and tolerance level'''.
+| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"|Then we define the function '''Jacobi Iteration''' with input arguments
@@ Line 171: / Line 176: @@
 '''endfunction'''
 | style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"|
-* We calculate the value for''' x k p one''' and then check if the '''relative error is lesser than tolerance level.'''
+* We calculate the value for''' x k p one''' and then check if the '''relative error''' is lesser than '''tolerance level.'''
 * If it is lesser than '''tolerance level''', we break the iteration and the solution is returned.
 * Finally we end the function.
 |-
@@ Line 207: / Line 221: @@
 Initial approximation nx1: '''<nowiki>[1;1]</nowiki>'''
-| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The '''initial values matrix''' is '''open square bracket one semi colon one close square bracket'''
+| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The '''initial values matrix''' is '''open square bracket one semi colon one close square bracket'''
 Press '''Enter'''.
@@ Line 241: / Line 255: @@
 The values for '''x one''' and '''x two''' are shown on the '''console'''.
 |-
@@ Line 375: / Line 391: @@
 * At each iteration, the value of '''x k p one''' gets updated.
 * Also, we check if '''relative error''' is lesser than specified '''tolerance level'''.
-* If it is, we '''break the iteration'''.
+* If it is, we break the iteration.
-* Then equate '''x k p one''' to the variable solution.
+* Then equate '''x k p one''' to the variable '''solution'''.
 * Finally, we end the function.
@@ Line 447: / Line 463: @@
-| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Finally we call the function by typing
+| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"|Finally we call the function by typing
 ''' G a u s s S e i d e l open paranthesis A comma b comma x zero comma M a x I t e r comma t o l close paranthesis'''