Linear Program Polynomial Interpolation Examples
Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. 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 at non-negative integer nodes to take care of any multi-choice parameter. After establishing interpolating polynomials of all multi-choice parameters, a mathematical programming problem is formulated. The formulated problem is treated as a nonlinear programming problem involving mixed integer type variables.
COLLEGE OF ARTS & SCIENCES MATHEMATICS Detailed course offerings (Time Schedule) are available for. Autumn Quarter 2017. This polynomial does what we want it to do, because when x = xj every one of the basis functions vanishes, except for Ln,j(x), which has value 1. Thus L(xj)= yj for every j and the polynomial interpolates each one of the data points in the original data set. Here is a set of data points.
It can be solved by using standard nonlinear programming software. Avicii Download Sample. Finally, a numerical example is presented to illustrate the solution procedure. • Previous article in issue • Next article in issue.
The simplest method of interpolation is to draw straight lines between the known data points and consider the function as the combination of those straight lines. This method, called linear interpolation, usually introduces considerable error. A more precise approach uses a polynomial function to connect the points. A is a mathematical expression comprising a sum of terms, each term including a variable or variables raised to a power and multiplied by a. The simplest polynomials have one variable.
Polynomials can exist in factored form or written out in full. For example: ( x - 4) ( x + 2) ( x + 10) x 2 + 2 x + 1 3 y 3 - 8 y 2 + 4 y - 2 The value of the largest exponent is called the degree of the polynomial. If a set of data contains n known points, then there exists exactly one polynomial of degree n-1 or smaller that passes through all of those points. The polynomial's graph can be thought of as 'filling in the curve' to account for data between the known points. This methodology, known as polynomial interpolation, often (but not always) provides more accurate results than linear interpolation. The main problem with polynomial interpolation arises from the fact that even when a certain polynomial function passes through all known data points, the resulting graph might not reflect the actual state of affairs.
It is possible that a polynomial function, although accurate at specific points, will differ wildly from the true values at some regions between those points. This problem most often arises when 'spikes' or 'dips' occur in a graph, reflecting unusual or unexpected events in a real-world situation. Computer Network In Hindi Notes more. Such anomalies are not reflected in the simple polynomial function which, even though it might make perfect mathematical sense, cannot take into account the chaotic nature of events in the physical universe.