This document discusses different interpolation methods:
- Interpolation finds values of a function between known x-values where the function values are given.
- Newton's forward and backward interpolation formulas are presented along with examples.
- Newton's divided difference interpolation uses a formula involving differences to find interpolating polynomials.
- Langrange's interpolation formula expresses the interpolating polynomial as a linear combination of basis polynomials defined in terms of the x-values. An example computing an interpolated value is shown.
Caco-2 cell permeability assay for drug absorption
Computational Methods for Mechanical Engineering Interpolation Techniques
1. S.N.PATEL INSTITUTE OF TECHNOLOGY
AND RESEARCH CENTRE
Computational Method for Mechanical Engineering
Prepared by :
Padhiyar Brijesh R.
(170490728009)
2. Interpolation
Interpolation means to find values of
function f(x) for an x between
different x-values x0, x1…, xn at
which the values of f(x) are given.
14. Example :
Find the polynomial of the lowest possible degree which assumes the values 3, 12,
15,-21 when x has the values 3, 2, 1,-1, respectively. Hence find f(0).
17. LANGRANGE’S INTERPOLATION
1 2
0
0 1 0 2 0
0 2
1
1 0 1 2 1
0 1
2
2 0 2 1 2
( )( )........( )
( )
( )( )........( )
( )( )........( )
( )( )........( )
( )( )........( )
+ .....
( )( )........( )
n
n
n
n
n
n
x x x x x x
F x y
x x x x x x
x x x x x x
y
x x x x x x
x x x x x x
y
x x x x x x
...
19. 1 2
0
0 1 0 2 0
0 2
1
1 0 1 2 1
0 1
2
2 0 2 1 2
( )( )........( )
( )
( )( )........( )
( )( )........( )
( )( )........( )
( )( )........( )
+ .....
( )( )........( )
n
n
n
n
n
n
x x x x x x
F x y
x x x x x x
x x x x x x
y
x x x x x x
x x x x x x
y
x x x x x x
...
(0.3−1)(0.3−3)(0.3−4)(0.3−7) (0.3−0)(0.3−3)(0.3−4)(0.3−7) (0.3−0)(0.3−1)(0.3−4)(0.3−7)
(0.3−0)(0.3−1)(0.3−3)(0.3−7) (0.3−0)(0.3−1)(0.3−3)(0.3−4)
(−1)(−3)(−4)(−7) (1)(-2)(−3)(−6) (3)(2)(−1)(−4)
(4)(3)(1)(−3) (4)(3)(6)(7)
*1+= *49+*3+
*813*129+
= 1.831