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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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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

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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

Mathematical Modeling and Simulation

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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

Mathematical Modeling and Simulation

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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

Mathematical Modeling and Simulation

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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

Mathematical Modeling and Simulation

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Colormap

Mathematical Modeling and Simulation

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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

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End

Mathematical Modeling and Simulation

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