Interpolation and Curve Fitting

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# Interpolation and Curve Fitting - PowerPoint PPT Presentation

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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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.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

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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
• griddata Example: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 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)

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End

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