Download presentation

Presentation is loading. Please wait.

Published bySteven Lyon Modified over 3 years ago

1
Prof. Muhammad Saeed ( Interpolation and Curve Fitting )

2
2M.Sc. Physics 1.Interpola tion a)Newton-Gregory Forward Formula Evenly Spaced Data

3
M.Sc. Physics3 a)Lagrange Polynomials (Cubic) Unevenly Spaced Data b)Divided Difference

4
M.Sc. Physics4 c)Cubic Spline For condition 1 (Natural Spline): 2(h 0 +h 1 )h1h1 0000 S1S1 f[x 1, x 2 ] - f[x 0,x 1 ] h1h1 2(h 1 +h 2 )h2h2 000 S2S2 f[x 2, x 3 ] - f[x 1,x 2 ] 0h2h2 2(h 2 +h 3 )h3h3 00 S3S3 f[x 3, x 4 ] - f[x 2,x 3 ] 00h3h3 2(h 3 +h 4 )h4h4 0 S4S4 = 6 f[x 4, x 5 ] - f[x 3,x 4 ] 000.. …. 0000 ….. 0000h n-2 2(h n-2 +h n-1 ) S n-1 f[x n-1, x n ] - f[x n-2,x n-1 ]

5
M.Sc. Physics5 2.Curve Fitting Least-Squares Approximations Functions to Fit 1) y = mx+c 2)Polynomial 2)y = ae bx 3)y = a log(x) + b 4) y = ax b 5) 6)y = ax 2 +bx y= a

6
M.Sc. Physics6 Nxx2x2 x3x3 ….xnxn a0a0 Y xx2x2 x3x3 x4x4 x n+1 a1a1 xY x2x2 x3x3 x4x4 x5x5 …..x n+2 a2a2 x2Yx2Y ……. …..… a3a3 = …. …………..… …. … …… ……..…. … xnxn x n+1 x n+2 x n+3 ….x 2n anan xnYxnY a)Polynomial Fit The Best Fit is determined by the minimum value of

7
M.Sc. Physics7 123456789101112131415 Weight 10.012.015.017.020.027.035.041.048.050.051.054.059.066.075.0 Height 0.750.860.951.081.121.261.351.511.551.601.631.671.711.781.85 Use W=aH b as mathematical model Problem: Weight to Height Ratio of Human Beings

8
M.Sc. Physics8 b)Line Regression

9
M.Sc. Physics9 c)Polynomial Regression m is the degree of polynomial

10
M.Sc. Physics10

Similar presentations

OK

STROUD Worked examples and exercises are in the text PROGRAMME F6 POLYNOMIAL EQUATIONS.

STROUD Worked examples and exercises are in the text PROGRAMME F6 POLYNOMIAL EQUATIONS.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on public speaking skills Ppt on campus recruiting systems Ppt on switching network Ppt on indian politics funny Ppt on set top box Ppt on new product development steps Ppt on p&g products rebate Ppt on world ozone day Ppt on major types of soil found in india Ppt on importance of plants life on earth