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

Sandhya.np14 at 18:24, 3 January 2018

2018-01-03T18:24:58Z

PoojaMoolya at 05:51, 10 March 2017

2017-03-10T05:51:41Z

Sandhya.np14 at 05:16, 2 March 2015

2015-03-02T05:16:56Z

Sandhya.np14 at 04:28, 2 March 2015

2015-03-02T04:28:57Z

Sandhya.np14 at 03:41, 2 March 2015

2015-03-02T03:41:38Z

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Gaurav at 12:30, 10 July 2014

2014-07-10T12:30:19Z

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Pratik kamble at 12:21, 10 July 2014

2014-07-10T12:21:51Z

PoojaMoolya: Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 | Welcome to the Spoken Tutorial on '''“Solving System of Linear Equations using Iterative Methods”…'

2014-03-12T05:35:43Z

Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 | Welcome to the Spoken Tutorial on '''“Solving System of Linear Equations using Iterative Methods”…'

New page

{| Border=1

|| Time

|| Narration

|-
| 00.01
|Dear Friends,

|-
| 00.02
| Welcome to the Spoken Tutorial on '''“Solving System of Linear Equations using Iterative Methods” '''

|-
| 00.10
| At the end of this tutorial, you will learn how to:

|-
|00.14
|Solve system of '''linear equations''' using '''iterative methods'''

|-
|00.18
|Develop '''Scilab code''' to solve '''linear equations'''

|-
| 00.22
|To record this tutorial, I am using

|-
|00.25
|'''Ubuntu 12.04''' as the operating system

|-
| 00.28
|and '''Scilab 5.3.3''' version

|-
| 00.33
| Before practising this tutorial, a learner should have basic knowledge of

|-
|00.38
|'''Scilab'''

|-
|00.39
| and '''Solving Linear Equations'''

|-
| 00.42
| For '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.

|-
| 00.50
| The first '''iterative method''' we will be studying is '''Jacobi method.'''

|-
|00.56
|Given a '''system of linear equations, with n equations and n unknowns'''

|-
|01.02
| We rewrite the equations such that ''' 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'''

|-
|01.24
|We assume values for each '''x of i'''

|-

|01.27

|Then we substitute the values in the equations obtained in the previous step.

|-

|01.34

|We continue the iteration until the solution converges.

|-

| 01.39

|Let us solve this example using '''Jacobi Method'''

|-

| 01.44
||Let us look at the code for '''Jacobi Method.'''

|-

| 01.48
|| We use '''format''' method to specify the format of the displayed answers on the '''Scilab console. '''

|-

|01.56

|| Here '''e''' denotes the answer should be in '''scientific notation.'''

|-

|02.01

| And '''twenty''' specifies the number of digits to be displayed.

|-
|02.06
|Then we use '''input''' function to get the values for

|-

|02.10

|'''the matrices coefficient matrix,'''

|-

|02.12

||'''right hand side matrix,'''

|-
|02.14
|'''initial values matrix,'''

|-
| 02.17
|'''maximum number of iteration and'''

|-

| 02.19
||'''convergence tolerance'''

|-

|02.22

||Then we use '''size''' function to check if '''A matrix''' is a '''square matrix.'''

|-

|02.29

| If it isn't, we use '''error function''' to display an error.

|-

|02.34

| We then check if '''matrix A''' is '''diagonally dominant.'''

|-

| 02.40

|| The first half calculates the sum of each row of the '''matrix.'''

|-
| 02.45
| Then it checks if twice the product of the '''diagonal element''' is greater than the sum of the elements of that row.

|-
|02.54
| If it isn't, an error is displayed using ''' error function. '''

|-
|03.01
| Then we define the function '''Jacobi Iteration''' with input arguments

|-
| 03.07
| '''A, b , x zero, '''

|-
| 03.09
|'''maximum iteration and tolerance level. '''

|-
| 03.14
|Here '''x zero''' is the '''initial values matrix. '''

|-
| 03.19
|We check if the size of '''A matrix''' and '''initial values matrix''' are compatible with each other.

|-
|03.28
| We calculate the value for '''x k p one''' and then check if the '''relative error''' is lesser than '''tolerance level.'''

|-
| 03.38
| If it is lesser than '''tolerance level''', we break the iteration and the solution is returned.
|-

| 03.45

|Finally we end the function.

|-

| 03.48
|| Let us save and execute the function.

|-

|03.51

||Switch to '''Scilab console. '''

|-

| 03.54
| Let us enter the values at each prompt.

|-

| 03.57

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

|-
|04.08
| Press '''Enter. '''

|-

| 04.10

| Then we type '''open square bracket eleven semicolon thirteen close square bracket'''

|-

|04.17

||Press '''Enter. '''

|-

|04.20

|The '''initial values matrix is open square bracket one semi colon one close square bracket'''

|-

| 04.28

| Press '''Enter.'''

|-

| 04.30

|The '''maximum number of iterations''' is twenty five.

|-

| 04.34

| Press '''Enter. '''

|-

| 04.36

| Let the '''convergence tolerance level be zero point zero zero zero zero one '''

|-

| 04.44

||Press '''Enter. '''

|-

| 04.46

||We call the function by typing
|-

| 04.48

||'''Jacobi Iteration open paranthesis A comma b comma x zero comma M a x I t e r comma t o l close paranthesis '''

|-

| 05.04

|Press '''Enter. '''

|-

| 05.06

|The values for '''x one''' and '''x two''' are shown on the '''console. '''

|-

|05.11

|The number of iterations are also shown.

|-

|05.14

| Let us now study '''Gauss Seidel method. '''

|-

| 05.19

| 'Given a '''system of linear equations,''' with '''n equations''' and ''' n unknowns '''

|-

|05.26

||We rewrite the equations for each unknown

|-

| 05.29

| by subtracting the other variables and their coefficients from the corresponding right hand side element.

|-

| 05.37

| Then we divide this by the '''coefficient a i i of the''' unknown variable' for that variable. '''

|-

| 05.45

|This is done for every given equation.

|-

| 05.49

|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 '''

|-

| 06.03

| In '''Gauss Seidel method,''' we over write the value of '''x of i k''' with '''x of i k plus one'''

|-

| 06.12

|Let us solve this example using '''Gauss Seidel Method'''

|-
| 06.17
| Let us look at the code for '''Gauss Seidel Method'''

|-
| 06.21
|The first line specifies the '''format''' of the displayed answer on the '''console''' using '''format function.'''

|-

| 06.29

| Then we use '''input function''' to get the values of

|-

| 06.32

| '''coefficient matrix, '''

|-

| 06.34

| '''right hand side matrix,'''

|-

| 06.36

| '''initial values of the variables matrix, '''

|-

| 06.38

| '''maximum number of iterations''' and

|-

| 06.40

| '''tolerance level'''

|-

| 06.43

| 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

|-

| 06.58

| We check if '''matrix A is square''' and the sizes of '''initial vector and matrix A''' are compatible using '''size and length function.'''

|-

| 07.10

|Then we start the iterations.

|-

| 07.13

|We equate the '''initial values vector x zero to x k. '''

|-

| 07.19

|We create a '''matrix of zeros''' with the same size of ''' x k''' and call it '''x k p one.'''

|-

| 07.28

|We solve for each equation to get the value of the '''unknown variable''' for that equation using '''x k p one. '''

|-

| 07.38

|At each iteration, the value of '''x k p one''' gets updated.

|-

| 07.44

|Also, we check if '''relative error''' is lesser than specified '''tolerance level.'''

|-

| 07.50

|If it is, we break the iteration.

|-

| 07.54
|Then equate '''x k p one''' to the ''' variable solution.'''
|-

| 07.59

|Finally, we end the function.

|-

| 08.02

|Let us save and execute the function.
|-

| 08.06

|Switch to '''Scilab console'''

|-

| 08.09

|For the first prompt, we type ''' matrix A.'''

|-

| 08.12

|Type '''open square bracket two space one semi colon five space seven close square bracket'''

|-

| 08.21

|Press '''Enter'''

|-

| 08.22

|For the next prompt,

|-

| 08.24

|type '''open square bracket eleven semi colon thirteen close square bracket'''

|-

| 08.31

|Press '''Enter. '''

|-

| 08.33

|We provide the values of '''initial value vector''' by typing

|-

| 08.38

|'''open square bracket one semicolon one close square bracket'''

|-

| 08.43

|Press '''Enter. '''

|-

| 08.45

|Then we specify the ''' maximum number of iterations''' to be twenty five

|-

| 08.50

|Press '''Enter. '''

|-

| 08.52

|Let us define '''tolerance level'' to be zero point zero zero zero zero one
|-

| 08.58

|Press '''Enter'''

|-

| 09.01

|Finally we call the function by typing

|-

| 09.04

|'''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'''

|-

| 09.24

|Press '''Enter'''.

|-

| 09.26

|The values of '''x one''' and '''x two''' are displayed.

|-

| 09.30

|The number of iterations to solve the same problem are lesser than '''Jacobi method.'''

|-

| 09.37

|Solve this problem on your own using '''Jacobi''' and '''Gauss Seidel methods'''

|-

| 09.43

|In this tutorial, we have learnt to:

|-

| 09.47

|Develop '''Scilab code''' for solving system of linear equations

|-

| 09.52

|Find the value of the '''unknown variables''' of a system of '''linear equations'''

|-
|09.58
| Watch the video available at the following link

|-

| 10.01

| It summarises the Spoken Tutorial project

|-

|10.04

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

|-

|10.09

||The spoken tutorial project Team

|-

|10.11

||Conducts workshops using spoken tutorials

|-

|10.15

||Gives certificates to those who pass an online test

|-

|10.18

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

|-

|10.25

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

|-

| 10.30

| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
|-

| 10.37

|More information on this mission is available at http://spoken-tutorial.org/NMEICT-Intro

|-

| 10.49

|This is Ashwini Patil signing off.

|-

|10.51

| Thank you for joining.

@@ Line 399: / Line 399: @@
 | 06:43
-| 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.
+| 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'''.
 |-

@@ Line 6: / Line 6: @@
 |-
 | 00:01
-|Dear Friends,
+|Dear Friends, Welcome to the Spoken Tutorial on '''Solving System of Linear Equations using Iterative Methods'''.
-−
-|-
-| 00:02
-| Welcome to the Spoken Tutorial on '''Solving System of Linear Equations using Iterative Methods'''.
 |-
@@ Line 42: / Line 38: @@
 |-
 |00:38
-|'''Scilab'''
+|'''Scilab''', and '''solving linear equations'''.
-−
-|-
-|00:39
-| and '''solving linear equations'''.
 |-
@@ Line 494: / Line 486: @@
 | 08:21
-|Press '''Enter'''.
+|Press '''Enter'''. For the next prompt,
-−
-|-
-−
-| 08:22
-−
-|For the next prompt,
 |-

@@ Line 179: / Line 179: @@
 |-
 | 03:09
-|'''maximum iteration and tolerance level.'''
+|'''maximum iteration''' and '''tolerance level'''.
 |-
@@ Line 195: / Line 195: @@
 |-
 | 03:38
-| If it is lesser than '''tolerance level''', we break the iteration and the solution is returned.
+| If it is lesser than '''tolerance level''', we '''break''' the iteration and the solution is returned.
 |-
 | 03:45
-|Finally we end the function.
+|Finally we '''end''' the function.
 |-
@@ Line 268: / Line 268: @@
 | 04:36
-| Let the '''convergence tolerance level be zero point zero zero zero zero one '''.
+| Let the '''convergence tolerance level be zero point zero zero zero zero one '''
 |-
@@ Line 371: / Line 371: @@
 | 06:29
-| Then we use '''input function''' to get the values of
+| Then we use '''input''' function to get the values of
 |-
@@ Line 455: / Line 455: @@
 | 07:50
-|If it is, we break the iteration.
+|If it is, we '''break''' the iteration.
 |-
@@ Line 465: / Line 465: @@
 | 07:59
-|Finally, we end the function.
+|Finally, we '''end''' the function.
 |-

@@ Line 147: / Line 147: @@
 |02:29
-| If it isn't, we use '''error function''' to display an error.
+| If it isn't, we use '''error''' function to display an error.
 |-
@@ Line 167: / Line 167: @@
 |-
 |02:54
-| If it isn't, an error is displayed using ''' error function. '''
+| If it isn't, an error is displayed using '''error''' function.
 |-
@@ Line 211: / Line 211: @@
 |03:51
-||Switch to '''Scilab console. '''
+||Switch to '''Scilab console.'''
 |-
@@ Line 315: / Line 315: @@
 | 05:19
-| Given a '''system of linear equations''' with '''n equations''' and ''' n unknowns '''
+| 'Given a '''system of linear equations''' with '''n equations''' and ''' n unknowns '''
 |-
@@ Line 365: / Line 365: @@
 |-
 | 06:21
-|The first line specifies the '''format''' of the displayed answer on the '''console''' using '''format function.'''
+|The first line specifies the '''format''' of the displayed answer on the '''console''' using '''format''' function.
 |-
@@ Line 413: / Line 413: @@
 | 06:58
-| We check if '''matrix A is square''' and the sizes of '''initial vector and matrix A''' are compatible using '''size and length function.'''
+| We check if '''matrix A is square''' and the sizes of '''initial vector and matrix A''' are compatible using '''size''' and '''length''' function.
 |-
@@ Line 601: / Line 601: @@
 | 09:47
-|Develop '''Scilab code''' for solving system of linear equations
+|Develop '''Scilab code''' for solving system of linear equations.
 |-

@@ Line 1: / Line 1: @@
 {| Border=1
-|| Time
+|'''Time'''
-|| Narration
+|'''Narration'''
 |-
-| 00.01
+| 00:01
 |Dear Friends,
 |-
-| 00.02
+| 00:02
 | Welcome to the Spoken Tutorial on '''“Solving System of Linear Equations using Iterative Methods” '''
 |-
-| 00.10
+| 00:10
 | At the end of this tutorial, you will learn how to:
 |-
-|00.14
+|00:14
 |Solve system of '''linear equations''' using '''iterative methods'''
 |-
-|00.18
+|00:18
 |Develop '''Scilab code''' to solve '''linear equations'''
 |-
-| 00.22
+| 00:22
 |To record this tutorial, I am using
 |-
-|00.25
+|00:25
 |'''Ubuntu 12.04''' as the operating system
 |-
-| 00.28
+| 00:28
 |and '''Scilab 5.3.3''' version
 |-
-| 00.33
+| 00:33
 | Before practising this tutorial, a learner should have basic knowledge of
 |-
-|00.38
+|00:38
 |'''Scilab'''
 |-
-|00.39
+|00:39
 | and '''Solving Linear Equations'''
 |-
-| 00.42
+| 00:42
 | For '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.
 |-
-| 00.50
+| 00:50
 | The first '''iterative method''' we will be studying is '''Jacobi method.'''
 |-
-|00.56
+|00:56
 |Given a '''system of linear equations, with n equations and n unknowns'''
 |-
-|01.02
+|01:02
 | We rewrite the equations such that ''' 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'''
 |-
-|01.24
+|01:24
 |We assume values for each '''x of i'''
@@ Line 73: / Line 73: @@
 |-
-|01.27
+|01:27
 |Then we substitute the values in the equations obtained in the previous step.
@@ Line 79: / Line 79: @@
 |-
-|01.34
+|01:34
 |We continue the iteration until the solution converges.
@@ Line 85: / Line 85: @@
 |-
-| 01.39
+| 01:39
 |Let us solve this example using '''Jacobi Method'''
@@ Line 91: / Line 91: @@
 |-
-| 01.44
+| 01:44
 ||Let us look at the code for '''Jacobi Method.'''
 |-
-| 01.48
+| 01:48
 || We use '''format''' method to specify the format of the displayed answers on the '''Scilab console. '''
 |-
-|01.56
+|01:56
 || Here '''e''' denotes the answer should be in '''scientific notation.'''
@@ Line 107: / Line 107: @@
 |-
-|02.01
+|02:01
 | And '''twenty''' specifies the number of digits to be displayed.
@@ Line 113: / Line 113: @@
 |-
-|02.06
+|02:06
 |Then we use '''input''' function to get the values for
@@ Line 119: / Line 119: @@
 |-
-|02.10
+|02:10
 |'''the matrices coefficient matrix,'''
@@ Line 125: / Line 125: @@
 |-
-|02.12
+|02:12
 ||'''right hand side matrix,'''
 |-
-|02.14
+|02:14
 |'''initial values matrix,'''
 |-
-| 02.17
+| 05:.17
 |'''maximum number of iteration and'''