Linear Program Polynomial Interpolation Equation
We consider a linear programming problem where the right hand side parameters are multi-choice in nature. In this paper, the multiple choices of a parameter are considered as functional values of an affine function at some non-negative integer nodes. An interpolating polynomial is formulated using functional values.
LAGRANGE'S INTERPOLATION FORMULA This is again an N th degree polynomial approximation formula to the function f(x), which is known at discrete points x i, i = 0, 1, 2... The formula can be derived from the Vandermonds determinant but a much simpler way of deriving this is from Newton's divided difference formula. If f(x) is approximated with an N th degree polynomial then the N th divided difference of f(x) constant and ( N+1) th divided difference is zero. That is f [x 0, x 1,... X n, x] = 0 From the second property of divided difference we can write f 0 + f n f x = 0 +... + (x 0 - x 1)...
(x 0 - x n)(x 0 - x) (x n - x 0) Cloning Of Sim Software. ... (x n - x n-1)(x n - x) (x - x 0)... (x - x n) or (x - x 1)... (x - x n) (x - x 0)... (x - x n-1) f(x) = f 0 +...
+ f n (x 0 - x 1)... (x 0 - x n) (x n - x 0)... (x n - x n-1) n ( n )f i S x - x j j = 0 (x i - x j) i = 0 j ยน 1 Since Lagrange's interpolation is also an N th degree polynomial approximation to f(x) and the N th degree polynomial passing through ( N+1) points is unique hence the Lagrange's and Newton's divided difference approximations are one and the same. However, Lagrange's formula is more convinent to use in computer programming and Newton's divided difference formula is more suited for hand calculations. Example: Compute f(0.3) for the data x 0 1 3 4 7 f 1 3 49 129 813 using Lagrange's interpolation formula (Analytic value is 1. Adobe Illustrator Cs2 Torrent Download With Keygen Generator there. 831) (x - x 1) (x - x 2)(x- x 3)(x - x 4) (x - x 0)(x - x 1) (x - x 2)(x - x 3) f(x) = f 0+...
+ f 4 (x 0 - x 1) (x 0 - x 2)(x 0 - x 3)(x 0 - x 4) (x 4 - x 0)(x 4 - x 1)(x 4 - x 2)(x 4 - x 3) (0.3 - 1)(0.3 - 3)(0. Dell Precision 870 Drivers. 3 - 4)(0.3 - 7) (0.3 - 0)(0.3 - 3)(0.3 - 4)(0.3 - 7) = 1+ 3 + (-1) (-3)(-4)(-7) 1 x (-2)(-3)(-6).