Curve fitting Guide, Meaning , Facts, Information and Description
In the philosophy of science, and science generally, and in statistics, the curve fitting problem is how to choose among an infinite number of curves that fit the graphically-represented data points, normally by finding a mathematical expression to create the curve.The simplest curve is said to be preferable. This is thought to be related to Occam's Razor in so far as there is a preference for simplicity among a family of curves just as there is a preference of simplicity among competing theories.
Commonly used procedures are least squares fitting, linear regression, and nonlinear regression. One of the difficulties in curve fitting is to choose the functional form of the data for parameter optimization. Computers are often used to perform curve fitting procedures. Computers do this by solving a system of equations to find the parameters of the function that minimize the squared error. The gradient descent algorithm is often used for this purpose.
Probabilistic algorithms such as RANSAC can be used to find a good fit for a sample set, given a parametrized model of the curve function.
Audi, R., Ed. (1996) The Cambridge Dictionary of Philosophy. Cambridge, Cambridge University Press. curve fitting problem p.172-173.
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