Scilab/C4/Interpolation/English-timed

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 xwhich 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.

Contributors and Content Editors

Gaurav, PoojaMoolya, Sandhya.np14