Advanced Mathematical Methods for Civil Engineering Applications
Wonsiri Punurai, PhDWonsiri Punurai, PhDDepartment of Civil EngineeringRoom 6391, EG Building 3Faculty of Engineering, Mahidol UniversityClass Web: www.egmu.net/~civil/wonsiri
Numerical techniques for interpolation & curve fitting
Interpolations
Linear InterpolationQuadratic InterpolationPolynomial InterpolationPiecewise Polynomial interpolation
Basic ideas - linear interpolation
Interpolation vs. Curve Fitting
Interpolation & Extrapolation
Linear Interpolation
Interpolations
Linear InterpolationQuadratic InterpolationPolynomial InterpolationPiecewise Polynomial interpolation
Quadratic Interpolation
Example: Quadratic Interpolation at x=2
Example: Quadratic Interpolation at x=2
Interpolations
Linear InterpolationQuadratic InterpolationPolynomial InterpolationPiecewise Polynomial interpolation
Polynomial Interpolation
Example
Vandermonde Matrix
Polynomials Wiggle
0 1 2 3 4 5 6 7 8 9 10-5
-4
-3
-2
-1
0
1
2
3
4
5
x
y
data2nd-order3rd-order4th-order5th-order
Piecewise Polynomial Interpolation
Matlab’s built-in interpolation functions
1 2 3 4 5 6 7 8 9 10-4
-3
-2
-1
0
1
2
3
4
1 2 3 4 5 6 7 8 9 10-4
-3
-2
-1
0
1
2
3
4
1 2 3 4 5 6 7 8 9 10-4
-3
-2
-1
0
1
2
3
4
1 2 3 4 5 6 7 8 9 10-4
-3
-2
-1
0
1
2
3
4
‘nearest’ ‘linear’
‘cubic’
‘spline’
