21 Aug 2007

KKKQ 3013KKKQ 3013PENGIRAAN BERANGKAPENGIRAAN BERANGKA

Week 7 ndash Interpolation amp Curve Fitting21 August 2007

800 am ndash 900 am

21 Aug 2007 Week 7 Page 2

Topics

1048713 Introduction1048713 Newton Interpolation Finite Divided Difference1048713 Lagrange Interpolation1048713 Spline Interpolation1048713 Polynomial Regression1048713 Multivariable Interpolation

21 Aug 2007 Week 7 Page 3

Tutorial Example 1 (adapted courtesy of ref [1])

Dynamic viscosity of water (10-3 Nsm2) is related to temperature T(oC) in the following manner

[1] Chapra SC amp Canale RP Numerical Methods for Engineers McGraw-Hill 5th ed (2006)

a) Estimate at T = 75oC using cubic spline interpolation

b) Use polynomial regression to determine a best fit parabola of the above data In addition determine the corresponding standard deviation

Based on this parabola what is at T = 75oC

21 Aug 2007 Week 7 Page 4

Tutorial Example 1

21 Aug 2007 Week 7 Page 5

Tutorial Example 1

21 Aug 2007 Week 7 Page 6

Tutorial Example 1

21 Aug 2007 Week 7 Page 7

Tutorial Example 1

21 Aug 2007 Week 7 Page 8

Tutorial Example 1

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 2

Topics

1048713 Introduction1048713 Newton Interpolation Finite Divided Difference1048713 Lagrange Interpolation1048713 Spline Interpolation1048713 Polynomial Regression1048713 Multivariable Interpolation

21 Aug 2007 Week 7 Page 3

Tutorial Example 1 (adapted courtesy of ref [1])

Dynamic viscosity of water (10-3 Nsm2) is related to temperature T(oC) in the following manner

[1] Chapra SC amp Canale RP Numerical Methods for Engineers McGraw-Hill 5th ed (2006)

a) Estimate at T = 75oC using cubic spline interpolation

b) Use polynomial regression to determine a best fit parabola of the above data In addition determine the corresponding standard deviation

Based on this parabola what is at T = 75oC

21 Aug 2007 Week 7 Page 4

Tutorial Example 1

21 Aug 2007 Week 7 Page 5

Tutorial Example 1

21 Aug 2007 Week 7 Page 6

Tutorial Example 1

21 Aug 2007 Week 7 Page 7

Tutorial Example 1

21 Aug 2007 Week 7 Page 8

Tutorial Example 1

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 3

Tutorial Example 1 (adapted courtesy of ref [1])

Dynamic viscosity of water (10-3 Nsm2) is related to temperature T(oC) in the following manner

[1] Chapra SC amp Canale RP Numerical Methods for Engineers McGraw-Hill 5th ed (2006)

a) Estimate at T = 75oC using cubic spline interpolation

b) Use polynomial regression to determine a best fit parabola of the above data In addition determine the corresponding standard deviation

Based on this parabola what is at T = 75oC

21 Aug 2007 Week 7 Page 4

Tutorial Example 1

21 Aug 2007 Week 7 Page 5

Tutorial Example 1

21 Aug 2007 Week 7 Page 6

Tutorial Example 1

21 Aug 2007 Week 7 Page 7

Tutorial Example 1

21 Aug 2007 Week 7 Page 8

Tutorial Example 1

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 4

Tutorial Example 1

21 Aug 2007 Week 7 Page 5

Tutorial Example 1

21 Aug 2007 Week 7 Page 6

Tutorial Example 1

21 Aug 2007 Week 7 Page 7

Tutorial Example 1

21 Aug 2007 Week 7 Page 8

Tutorial Example 1

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 5

Tutorial Example 1

21 Aug 2007 Week 7 Page 6

Tutorial Example 1

21 Aug 2007 Week 7 Page 7

Tutorial Example 1

21 Aug 2007 Week 7 Page 8

Tutorial Example 1

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 6

Tutorial Example 1

21 Aug 2007 Week 7 Page 7

Tutorial Example 1

21 Aug 2007 Week 7 Page 8

Tutorial Example 1

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 7

Tutorial Example 1

21 Aug 2007 Week 7 Page 8

Tutorial Example 1

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 8

Tutorial Example 1

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 9

Tutorial Example 1

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x

21 Aug 2007 Week 7 Page 10

Tutorial Example 1 (using MATLAB)

gtgt x=[0 5 10 20 30]

x =

0 5 10 20 30

gtgt y=[1787 1519 1307 1002 07975]

y =

17870 15190 13070 10020 07975

gtgt a=interp1(xy75spline)

a =

14069

gtgt p=polyfit(xy2)

p =

00007 -00534 17784

gtgt b=polyval(p75)

b =

14172

Prediction using cubic spline interpolation

Coefficient for best fit quadratic equation ie a2 a1 and a0 in descending powers of x