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Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
here is a simple example using the free Pari-GP program (or can use calculator) and basic matrix ops: given a data set (x,y) (2,5),(3,10) and (4,19) to solve to a presumed quadratic fit, a=[1,2,4;1,3,9;1,4,16] : b=[5;10;19] c=matsolve(a,b) returns [7 -5 2 ] y=2x^2-5x+7. One can then evaluate this in a spreadsheet/plot for adequacy of fit
TableCurve 2D is a linear and non-linear Curve fitting software package for engineers and scientists that automates the curve fitting process and in a single processing step instantly fits and ranks 3,600+ built-in frequently encountered equations enabling users to easily find the ideal model to their 2D data within seconds.
A polynomial function is one that has the form = + + + + + where n is a non-negative integer that defines the degree of the polynomial. A polynomial with a degree of 0 is simply a constant function; with a degree of 1 is a line; with a degree of 2 is a quadratic; with a degree of 3 is a cubic, and so on.
Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points. This results in a continuous curve, with a discontinuous derivative (in general), thus of differentiability class.
(defun integrate-composite-booles-rule (f a b n) "Calculates the composite Boole's rule numerical integral of the function F in the closed interval extending from inclusive A to ...
Any series of 4 distinct points can be converted to a cubic Bézier curve that goes through all 4 points in order. Given the starting and ending point of some cubic Bézier curve, and the points along the curve corresponding to t = 1/3 and t = 2/3, the control points for the original Bézier curve can be recovered. [9]
It is assumed that the value of a function f defined on [,] is known at + equally spaced points: < < <.There are two classes of Newton–Cotes quadrature: they are called "closed" when = and =, i.e. they use the function values at the interval endpoints, and "open" when > and <, i.e. they do not use the function values at the endpoints.