Scilab/C4/Interpolation/Gujarati

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.

Contributors and Content Editors

Jyotisolanki