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’