# Interpolation and Curve Fitting - PowerPoint PPT Presentation

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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

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Interpolation and Curve Fitting

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Mathematical Modeling and Simulation

## Interpolation and Curve Fitting

Using

MATLAB

• 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

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• ……..Polynomials:

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

• Example: Poly_09.m

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

• Example: Poly_10.mc 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

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• 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

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• 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

• griddataExample:RandomDataInterp_04

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• 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

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Colormap

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Test Matrices:

binomial cauchy chebspec chebvand

chow circul clement compar

fiedler forsythe frankgearmat

gcdmat grcar hanowa house

invhess invol ipjfact jordbloc

kahan kms krylovlauchli

lehmer leslie lesp lotkin

minij moler neumann orthog

parter pei poisson prolate

randcolu randcorr randhessrandjorth

rando randsvd redheff riemann

ris smoke toeppd tridiag

triw wathen wilk

A=gallery(‘binomial’, n)

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End

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