Curve Fitting

Curve fitting equation:

Introduction to curve fitting equation:

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data.
The study of ways of constructing functions whose graphs are curves that "best" approximates a given collection of points.We consider approximations by linear functions, polynomials of degree 2 or 3 and exponential functions using the method of least squares. After working through these materials, the student should be able

* to calculate using a graphing calculator or computer software the least squares line, parabola or third degree equation which best fits data.


Curve Fitting Equation:

Built-in curves are able to be use as an assist for data revelation, near assume value of a purpose wherever no data are obtainable; also to go over the associations with two or else further variables. Extrapolation illustrates to the make use of a fixed curve away from the collection of the practical data, with is the topic to a larger degree of indecision given that it might reproduce the way use to make the curve as greatly when it reproduce the experiential data.



Equation for Curve Fitting:

Permit establish through a 1st degree polynomial equation:

y=ax+b

This be a line through slope a. We identify to a line determination attach whichever two points. Thus, a 1st degree polynomial equation is an accurate fit during whichever two points.

Condition we raise the order of the equation toward a next degree polynomial, we obtain:

y=ax2+bx+c

Determination accurately fit an easy curve toward three points.

But we enlarge the order of the equation toward a 3rd degree polynomial, we obtain:

y=ax3+bx2+cx+d

These resolve accurately well four points.

A further common statement would exist toward declare it resolve accurately well four constraints. Every constraint be able to be a point, angle, otherwise curvature. Angle with curving constraints is mainly a lot additional toward the split ends of a curve; also during such belongings be call end conditions.

The curve fit for the polynomial equation is

Y (x) = P(x, n) = a0 + a1*x + a2*x2 ... + ... an*x n

The curve fit for the nonlinear approximation is

F(y) = a0*f0(x) + a1*f1(x) + ... + an*fn (x)

Hope you like the above example of Curve Fitting.Please leave your comments, if you have any doubts.