PoojaMoolya at 05:48, 10 March 2017

2017-03-10T05:48:05Z

Sandhya.np14 at 09:24, 2 March 2015

2015-03-02T09:24:49Z

Sandhya.np14 at 09:22, 2 March 2015

2015-03-02T09:22:19Z

Sandhya.np14 at 06:53, 2 March 2015

2015-03-02T06:53:10Z

Sandhya.np14 at 05:35, 2 March 2015

2015-03-02T05:35:56Z

Sandhya.np14 at 05:34, 2 March 2015

2015-03-02T05:34:51Z

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Gaurav at 04:53, 11 July 2014

2014-07-11T04:53:46Z

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PoojaMoolya: Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 | Welcome to the Spoken Tutorial on '''“Numerical Interpolation” ''' |- | 00.06 | At the end of th…'

2014-03-12T10:14:11Z

Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 | Welcome to the Spoken Tutorial on '''“Numerical Interpolation” ''' |- | 00.06 | At the end of th…'

New page

{| Border=1

|| Time

|| Narration

|-
| 00.01
|Dear Friends,

|-
| 00.02
| Welcome to the Spoken Tutorial on '''“Numerical Interpolation” '''

|-
| 00.06
| At the end of this tutorial, you will learn how to:

|-
|00.10
|Develop '''Scilab code''' for different '''Numerical Interpolation algorithms'''

|-
|00.16
|Calculate new value of '''function''' from given '''data points'''

|-
| 00.21
|To record this tutorial, I am using

|-
|00.24
|'''Ubuntu 12.04''' as the operating system

|-
| 00.27
|and '''Scilab 5.3.3''' version

|-
| 00.31
| To practise this tutorial, a learner should have

|-
|00.34
|basic knowledge of '''Scilab'''

|-
|00.36
|and should know '''Numerical Interpolation'''

|-
| 00.40
| To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website. '''Spoken Tutorial''' website.

|-
| 00.47
| '''Numerical interpolation''' is a method of

|-
|00.51
|constructing new '''data points'''

|-
|00.53
| within the range of a '''discrete set''' of known '''data points.'''

|-

|00.59

|We can solve '''interpolation''' problems using '''numerical methods.'''

|-

|01.05

|In '''Lagrange interpolation,'''

|-

| 01.07

|We pass a '''polynomial''' of '''degree N – 1''' through '''N''' points.

|-

| 01.12
||Then, we find the unique '''N order polynomial y of x'''which '''interpolates''' the '''data''' samples.

|-

|01.22

|| We are given the '''natural logarithm''' values for nine, nine point five and eleven.

|-

|01.29

| We have to find the value of '''natural logarithm''' of nine point two.

|-
|01.35
|Let us solve this problem using '''Lagrange interpolation method.'''

|-

|01.41

|Let us look at the code for '''Lagrange interpolation.'''

|-

|01.46

||We define the function '''Lagrange''' with '''arguments x zero, x, f and n.'''

|-
|01.53
|'''X zero''' is the unknown '''interpolation point.'''

|-
| 01.57
|'''x''' is the '''vector''' containing the '''data points.'''

|-

| 02.01
|'''f''' is the '''vector''' containing the values of the '''function''' at correspoding '''data points.'''

|-

|02.08

||And '''n''' is the '''order''' of the '''interpolating polynomial.'''
|-

|02.14

| We use '''n''' to initialize '''m''' and '''vector N.'''

|-

|02.19

| The order of the '''interpolating polynomial''' determines the number of '''nodes''' created.

|-

| 02.25

|| Then, we apply '''Lagrange interpolation formula'''

|-
| 02.29
| to find the value of the '''numerator''' and '''denominator.'''

|-
|02.35
| Then we divide the '''numerator''' and '''denominator''' to get the value of '''L.'''

|-
|02.41
| We use '''L''' to find the value of the function '''y''' at the given data point.

|-
| 02.48
| Finally we display the value of '''L''' and '''f of x.'''

|-
| 02.53
|Let us save and execute the file

|-
| 02.57
|Switch to '''Scilab console''' to solve the example problem.

|-
| 03.02
|Let us define the '''data points vector.'''

|-
|03.05
| On the '''console''' type,

|-
| 03.07
|''' x equal to open square bracket nine point zero comma nine point five comma eleven point zero close square bracket.'''

|-

| 03.18

|Press '''Enter'''

|-

| 03.21
||Then type '''f equal to open square bracket two point one nine seven two comma two point two five one three comma two point three nine seven nine close square bracket'''

|-

|03.39

||Press '''Enter '''

|-

| 03.41
| Then type '''x zero equal to nine point two'''

|-

| 03.46

| Press '''Enter'''

|-

| 03.48

| Let us use a '''quadratic polynomial interpolating polynomial.'''

|-

|03.53

||Type '''n equal to two'''

|-

|03.58

|Press '''Enter'''

|-

| 04.00

| To call the '''function,''' type

|-

| 04.02

|'''y equal to Lagrange open paranthesis x zero comma x comma f comma n close paranthesis'''

|-

| 04.14

| Press '''Enter. '''

|-

| 04.16

| The value of the function '''y at x equal to nine point two''' is displayed.

|-

| 04.22

||Let us look at '''Newton's Divided Difference Method.'''

|-

| 04.26

||In this method, '''Divided Differences recursive method''' is used.

|-

| 04.32

||It uses lesser number of '''computation''' than '''Lagrange method.'''

|-

| 04.38

|In spite of this, the same '''interpolating polynomial,''' as in '''Lagrange method,''' is generated.

|-

| 04.47

|Let us solve this example using '''Divided Difference method.'''

|-

|04.52

|We are given the '''data points''' and

|-

| 04.54

| the corresponding values of the '''function''' at those '''data points.'''

|-

| 05.00

| We have to find the value of the '''function''' at '''x equal to three.'''

|-

| 05.05

| Let us look at the code for '''Newton Divided Difference method. '''

|-

| 05.11

|Open the file '''Newton underscore Divided dot sci''' on '''Scilab Editor.'''

|-

| 05.18

|We define the '''function Newton underscore Divided''' with '''arguments x, f''' and '''x zero.'''

|-

| 05.29

| '''x''' is a '''vector''' containing the '''data points,'''

|-

| 05.33

|'''f''' is the corresponding '''function value''' and

|-
| 05.36
| '''x zero''' is the unknown '''interpolation point.'''

|-
| 05.41
|We find the length of '''vector''' and then equate it to '''n.'''
|-

| 05.46

| The first value of '''vector''' is equated to '''a of one.'''

|-

| 05.51

| Then we apply '''divided difference algorithm''' and compute the '''divided difference table.'''

|-

| 05.57

| Then we find the '''coefficient list''' of the '''Newton polynomial'''

|-

| 06.03

| We sum the '''coefficient list''' to find the value of the '''function''' at given '''data point.'''

|-

| 06.10

| Save and execute the file '''Newton underscore Divided dot sci.'''

|-

| 06.16

| Switch to '''Scilab console'''
|-

| 06.19

|Clear the screen by typing '''c l c'''

|-

| 06.22

|Press '''Enter.'''

|-

| 06.24

|Let us enter the '''data points vector'''

|-

| 06.27

|Type '''x equal to open square bracket two comma two point five comma three point two five comma four close square bracket '''

|-

| 06.39

|Press '''Enter.'''

|-

| 06.41

|Then type values of the '''function'''
|-

| 06.44

|'''f equal to open square bracket zero point five comma zero point four comma zero point three zero seven seven comma zero point two five close square bracket'''

|-

| 07.01
|Press '''Enter. '''
|-

| 07.03

|Type '''x zero equal to three'''

|-

| 07.06

|Press '''Enter.'''

|-

| 07.08

|Then call the '''function''' by typing

|-

| 07.11

|'''i p equal to Newton underscore Divided open parenthesis x comma f comma x zero close parenthesis'''

|-

| 07.23

|Press '''Enter.'''

|-

| 07.25

|The value of '''y at x equal to three''' is shown.

|-

| 07.30

|Let us summarize this tutorial.

|-

| 07.33

|In this tutorial,

|-

| 07.34

|we have learnt to develop '''Scilab''' code for '''interpolation methods.'''

|-

| 07.40

|We have also learnt to find the value of a '''function''' at new '''data point.'''

|-

| 07.46

|Solve this problem on your own using '''Lagrange method and Newton's Divided Difference method.'''

|-
|07.54
| Watch the video available at the link shown below

|-

| 07.57

| It summarises the Spoken Tutorial project

|-

|08.00

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

|-

|08.05

||The spoken tutorial project Team

|-

|08.07

||Conducts workshops using spoken tutorials

|-

|08.10

||Gives certificates to those who pass an online test

|-

|08.14

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

|-

|08.22

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

|-

| 08.26

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

| 08.33

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

|-

| 08.38

|This is Ashwini Patil signing off.

|-

|08.41

| Thank you for joining.

@@ Line 6: / Line 6: @@
 |-
 | 00:01
-|Dear Friends,
+|Dear Friends, Welcome to the Spoken Tutorial on '''Numerical Interpolation'''.
-−
-|-
-| 00:02
-| Welcome to the Spoken Tutorial on '''Numerical Interpolation'''.
 |-
@@ Line 467: / Line 463: @@
 | 07:33
-|In this tutorial,
+|In this tutorial, we have learnt to develop '''Scilab''' code for '''interpolation methods.'''
-−
-|-
-−
-| 07:34
-−
-|we have learnt to develop '''Scilab''' code for '''interpolation methods.'''
 |-

@@ Line 164: / Line 164: @@
 |-
 | 02:48
-| Finally we display the value of '''L''' and '''f of x.'''
+| Finally we display the value of '''L''' and '''f of x''' f(x).
 |-
 | 02:53
-|Let us save and execute the file.
+|Let us '''Save and execute''' the file.
 |-

@@ Line 340: / Line 340: @@
 |-
 | 05:41
-|We find the length of '''vector''' and then equate it to '''n.'''
+|We find the '''length''' of '''vector''' and then equate it to '''n.'''
 |-
 | 05:46
-| The first value of '''vector''' is equated to '''a of one.'''
+| The first value of '''vector''' is equated to '''a of one''' a(1).
 |-
@@ Line 363: / Line 363: @@
 | 06:03
-| We sum the '''coefficient list''' to find the value of the '''function'''  at given '''data point.'''
+| We '''sum''' the '''coefficient list''' to find the value of the '''function'''  at given '''data point.'''
 |-
@@ Line 369: / Line 369: @@
 | 06:10
-| Save and execute the file '''Newton underscore Divided dot sci.'''
+| '''Save and execute''' the file '''Newton underscore Divided dot sci.'''
 |-
@@ Line 443: / Line 443: @@
 | 07:11
-|'''i p equal to Newton underscore Divided open parenthesis x comma f comma x zero close parenthesis'''
+|'''I P equal to Newton underscore Divided open parenthesis x comma f comma x zero close parenthesis'''
 |-

@@ Line 50: / Line 50: @@
 |-
 | 00:40
-| To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.  '''Spoken Tutorial''' website.
+| To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.
-−
 |-
 | 00:47
@@ Line 399: / Line 398: @@
 | 06:27
-|Type: '''x equal to open square bracket two comma two point five comma three point two five comma four close square bracket '''
+|Type: '''x equal to open square bracket two comma two point five comma three point two five comma four close square bracket'''
 |-

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Scilab/C4/Interpolation/English-timed - Revision history