Interpolation and curve fitting
Download
1 / 9

Interpolation and Curve Fitting - PowerPoint PPT Presentation


  • 161 Views
  • Uploaded on

Mathematical Modeling and Simulation. Interpolation and Curve Fitting. Using MATLAB. Prof. Muhammad Saeed. Polynomials: p = [1 -2 3 6] , y = polyval (p, x) %definition Examples: Poly_01.m , Poly_02.m c = conv ( a,b ) % multiplication Example: Poly_03.m

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Interpolation and Curve Fitting' - neil


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Interpolation and curve fitting

Mathematical Modeling and Simulation

Interpolation and Curve Fitting

Using

MATLAB

Prof. Muhammad Saeed


  • Polynomials:

    • p = [1 -2 3 6] , y = polyval(p, x)%definition

    • Examples:Poly_01.m , Poly_02.m

    • c = conv(a,b) % multiplication

    • Example:Poly_03.m

    • [q, r]=deconv(a,b)% division

    • Example: Poly_04.m

    • c = polyder(p) %derivative

    • Example:Poly_05.m

    • c = polyder(a,b) %derivative of product

    • Example: Poly_06.m

    • [n,d] = polyder(a,b) %derivative of division

    • Example: Poly_07.m

Mathematical Modeling and Simulation

2


  • intgrl = polyint(p) integral of polynomial ‘p’

  • Example: Poly_09.m

  • intgrl = polyint(p, c) integral of polynomial ‘p’

  • Example: Poly_10.m c a constant of integration

  • r = roots(p)roots of polynomial ‘p’

  • Example: Poly_11.m

  • p = poly(r) polynomial of roots ‘r’

  • Example: Poly_12.m

  • p = poly(x)x must be a square matrix

  • Example: Poly_13.mp is characteristic polynomial

Mathematical Modeling and Simulation

3


  • Interpolation I:

    • interp1(x,y,a), Example:InterpFit_01.m

    • interp1(x,y,a,’linear’), InterpFit_01b.m

    • interp1(x,y,a,’cubic’),

    • interp1(x,y,a,’spline’),

    • Interp1(x,y,a,’nearest’)

    • interp2(x,y,z,a,b,’ …….. ‘) , [xx,yy]=meshgrid(x,y), mesh()

    • Example: InterpFit_02.m

    • interp3

    • interp1q, %it is quicker than ‘interp1’ on non-uniformly

    • spaced data because it does no input checking

    • interpft,

    • interpn

Mathematical Modeling and Simulation

4


  • Interpolation II:

    • tri=delaunay(x,y), trimesh(tri,x,y,z),

    • tsearch(x,y,tri,[x b],[c d]), dsearch

    • Example:RandomDataInterp_01

    • [pts,area] = convhull(x,y) Example: RandomDataInterp_02

    • voronoi(x,y) Example:RandomDataInterp_03

    • griddata Example:RandomDataInterp_04

Mathematical Modeling and Simulation

5


  • Curve Fitting:

    • p = polyfit(x,y,n) Example: PolyFits_01.m

    • [p, s] = polyfit(x,y,n)

    • [p,s,μ ] = polyfit(x,y,n)

    • yi = spline(x,y,xi) Example: SplineFits_01.m

    • pp=spline(x,y), yi=ppval(pp,xi)

    • hp = pchip(x,y), Example: HermiteSplineFits_01.m

Mathematical Modeling and Simulation

6


Colormap

Mathematical Modeling and Simulation

7


Test Matrices:

binomial cauchy chebspec chebvand

chow circul clement compar

condex cycol dorr dramadah

fiedler forsythe frank gearmat

gcdmat grcar hanowa house

invhess invol ipjfact jordbloc

kahan kms krylov lauchli

lehmer leslie lesp lotkin

minij moler neumann orthog

parter pei poisson prolate

randcolu randcorr randhess randjorth

rando randsvd redheff riemann

ris smoke toeppd tridiag

triw wathen wilk

A=gallery(‘binomial’, n)

Mathematical Modeling and Simulation

8


End

Mathematical Modeling and Simulation

9


ad