Interpolation and

Curve FittingProf. Muhammad Saeed

Mathematical Modeling and Simulation

UsingMATLABMATLAB

22Mathematical Modeling and Simulation

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)%derivativeExample: Poly_05.m

c = polyder(a,b)%derivative of productExample: Poly_06.m

[n,d] = polyder(a,b) %derivative of divisionExample: Poly_07.m

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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.m p is characteristic polynomial

……..Polynomials:

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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

interp3interp1q, %it is quicker than ‘interp1’ on non-uniformly

spaced data because it does no input checkinginterpft, 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

Colormap

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Test Matrices:

binomial cauchy chebspec chebvandchow circul clement comparcondex cycol dorr dramadahfiedler forsythe frank gearmatgcdmat grcar hanowa houseinvhess invol ipjfact jordblockahan kms krylov lauchlilehmer leslie lesp lotkinminij moler neumann orthogparter pei poisson prolaterandcolu randcorr randhess randjorthrando randsvd redheff riemannris smoke toeppd tridiagtriw wathen wilk

A=gallery(‘binomial’, n)

End

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