Scilab/C4/Interpolation/Gujarati - Revision history

Jyotisolanki at 11:00, 30 December 2015

2015-12-30T11:00:45Z

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Jyotisolanki at 09:42, 30 December 2015

2015-12-30T09:42:08Z

Jyotisolanki at 07:25, 30 December 2015

2015-12-30T07:25:20Z

Jyotisolanki: 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 o..."

2015-12-30T07:16:33Z

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 o..."

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 practice 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.
|-
| 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 corresponding '''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''' f(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 parenthesis x zero comma x comma f comma n close parenthesis'''

|-

| 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''' a(1).

|-

| 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 summarizes 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 47: / Line 47: @@
 |-
 |00:36
-| '''Numerical Interpolation''' નું સામન્ય જ્ઞાન હોવું જોઈએ. .
+| '''Numerical Interpolation''' નું સામન્ય જ્ઞાન હોવું જોઈએ.
 |-
 | 00:40
-| To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.
+| સાઈલેબ માટે સ્પોકન ટ્યુટોરિયલ વેબ સાઈટ પર ઉપલબ્ધ સંબંધિત ટ્યુટોરિયલ જુઓ.
 |-
 | 00:47
-| '''Numerical interpolation''' is a method of
+| '''Numerical interpolation''' મેળવેલ '''data points''' ના  '''discrete set''' ના રેંજના અંદર  ડેટા પોઈન્ટસ ને બનાવવાનું એક મેથડ છે.
 |-
@@ Line 68: / Line 63: @@
 |00:59
-|We can solve '''interpolation''' problems using '''numerical methods.'''
+|આપણે '''numerical methods.''' નો ઉપયોગ કરીને  '''interpolation''' ના પ્રશ્નને હલ કરી શકીએ છીએ.
 |-
@@ Line 74: / Line 69: @@
 |01:05
-|In '''Lagrange interpolation,'''
+| '''Lagrange interpolation,'''  માં
 |-
@@ Line 80: / Line 75: @@
 | 01:07
-|We pass a '''polynomial''' of '''degree N – 1''' through '''N''' points.
+|આપણે '''N''' પોઈન્ટસ થી  '''N – 1'''  ના   '''polynomial''' ને પાસ કરીએ છીએ
 |-
 | 01:12
-||Then, we find the unique '''N order polynomial y of x''' which '''interpolates''' the '''data''' samples.
+||  પછી આપણે વિશિષ્ટ '''N order polynomial y of x''' ને મેળવીએ છીએ જે ડેટા સેમ્પલને ઇન્ટરપોલેટ કરે છે.
 |-
@@ Line 91: / Line 86: @@
 |01:22
-|| We are given the '''natural logarithm'''  values for nine, nine point five and eleven.
+||  આપણે '''nine, nine point five અને eleven'''  ની '''natural logarithm'''  વેલ્યુ આપેલ છે.
 |-
@@ Line 97: / Line 92: @@
 |01:29
-| We have to find the value of '''natural logarithm''' of nine point two.
+| આપણે '''nine point two''' ની '''natural logarithm'''  વેલ્યુ મેળવવાની છે.
 |-
 |01:35
-|Let us solve this problem using '''Lagrange interpolation method.'''
+|ચાલો  '''Lagrange interpolation method.''' (લેગરેંગ ઇન્ટરપોલેશન મેથડ) નો ઉપયોગ કરીને આ સવાલને હલ કરીએ.
 |-
@@ Line 107: / Line 102: @@
 |01:41
-|Let us look at the code for  '''Lagrange interpolation.'''
+|ચાલો  '''Lagrange interpolation.'''  (લેગરેંગ ઇન્ટરપોલેશન મેથડ) ના માટે કોડ જોઈએ.
 |-
@@ Line 113: / Line 108: @@
 |01:46
-||We define the function '''Lagrange''' with '''arguments x zero, x, f and n.'''
+||આપણે '''arguments x zero, x, f અને  n.'''  ના સાથે  '''Lagrange''' (લેગરેંગ)  ફંક્શનને વ્યાખ્યાયિત કરીએ છીએ.
 |-

@@ Line 6: / Line 6: @@
 |-
 | 00:01
-|Dear Friends,
+|નમસ્તે મિત્રો,
 |-
 | 00:02
-| Welcome to the Spoken Tutorial on '''Numerical Interpolation'''.
+|  '''Numerical Interpolation'''  પરના આ સ્પોકન ટ્યુટોરિયલમાં તમારું સ્વાગત છે. .
 |-
 | 00:06
-| At the end of this tutorial, you will learn how to:
+| આ ટ્યુટોરીયલના અંતમાં તમે શીખીશું કેવી રીતે:
 |-
 |00:10
-|Develop '''Scilab code''' for different '''Numerical Interpolation algorithms'''
+| વિવિધ  '''Numerical Interpolation algorithms''' ના માટે સાઈલેબ કોડ કેવી રીતે બનાવાય છે.
 |-
 |00:16
-|Calculate new value of '''function''' from given '''data points'''.
+| આપેલ પોઈન્ટસ થી '''function''' ની નવી વેલ્યુની ગણતરી કરવી.
 |-
 | 00:21
-|To record this tutorial, I am using
+|આ ટ્યુટોરિયલ રિકોર્ડ કરવા માટે હું ઉપયોગ કરી રહી છું,
 |-
 |00:24
-|'''Ubuntu 12.04''' as the operating system
+| '''Scilab 5.3.3''' વર્જનના સાથે.
 |-
 | 00:27
-|and '''Scilab 5.3.3''' version.
+| '''Ubuntu 12.04''' ઓપરેટીંગ સીસ્ટમ
 |-
 | 00:31
-| To practice this tutorial, a learner should have
+| આ ટ્યુટોરિયલ ના અભ્યાસ પહેલા શીખનારને
 |-
 |00:34
-|basic knowledge of '''Scilab'''
+|'''Scilab'''  અને
 |-
 |00:36
-|and should know '''Numerical Interpolation'''.
+| '''Numerical Interpolation''' નું સામન્ય જ્ઞાન હોવું જોઈએ. .
 |-