Curve Fitting Task
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A Curve Fitting Task is a function fitting task that is restricted to surface functions.
- AKA: Metric Space Approximation.
- Context:
- It can range from being an Algebraic Function Fitting Task to being a Non-Algebraic Function Fitting Task.
- It can be solved by a Curve Fitting System (that implements a Curve Fitting Algorithm).
- Example(s):
- Counter-Example(s):
- See: Regression Task, Linear Programming Task.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/curve_fitting Retrieved:2015-6-14.
- 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" function is constructed that approximately fits the data. A related topic is regression analysis, [10] [11] which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, [12] [13] to infer values of a function where no data are available, [14] and to summarize the relationships among two or more variables. [15] Extrapolation refers to the use of a fitted curve beyond the range of the observed data, [16] and is subject to a degree of uncertainty [17] since it may reflect the method used to construct the curve as much as it reflects the observed data.
- ↑ Sandra Lach Arlinghaus, PHB Practical Handbook of Curve Fitting. CRC Press, 1994.
- ↑ William M. Kolb. Curve Fitting for Programmable Calculators. Syntec, Incorporated, 1984.
- ↑ S.S. Halli, K.V. Rao. 1992. Advanced Techniques of Population Analysis. isbn 0306439972 Page 165 (cf. … functions are fulfilled if we have a good to moderate fit for the observed data.)
- ↑ [http://books.google.com/books?id=SI-VqAT4_hYC The Signal and the Noise: Why So Many Predictions Fail-but Some Don't. By Nate Silver
- ↑ Data Preparation for Data Mining: Text. By Dorian Pyle.
- ↑ Numerical Methods in Engineering with MATLAB®. By Jaan Kiusalaas. Page 24.
- ↑ Numerical Methods in Engineering with Python 3. By Jaan Kiusalaas. Page 21.
- ↑ Numerical Methods of Curve Fitting. By P. G. Guest, Philip George Guest. Page 349.
- ↑ See also: Mollifier
- ↑ Fitting Models to Biological Data Using Linear and Nonlinear Regression. By Harvey Motulsky, Arthur Christopoulos.
- ↑ Regression Analysis By Rudolf J. Freund, William J. Wilson, Ping Sa. Page 269.
- ↑ Visual Informatics. Edited by Halimah Badioze Zaman, Peter Robinson, Maria Petrou, Patrick Olivier, Heiko Schröder. Page 689.
- ↑ Numerical Methods for Nonlinear Engineering Models. By John R. Hauser. Page 227.
- ↑ Methods of Experimental Physics: Spectroscopy, Volume 13, Part 1. By Claire Marton. Page 150.
- ↑ Encyclopedia of Research Design, Volume 1. Edited by Neil J. Salkind. Page 266.
- ↑ Community Analysis and Planning Techniques. By Richard E. Klosterman. Page 1.
- ↑ An Introduction to Risk and Uncertainty in the Evaluation of Environmental Investments. DIANE Publishing. Pg 69
- (Allain, 2015) ⇒ Rhett Allain. (2015). “An Ode to the Graph, Physics’ Underappreciated Workhorse.” In: Wired, 2015-06-03
- QUOTE: … if you fit a linear equation to that data, what would the slope represent? ...
- Plotting data as a linear graph is a great way to examine the validity of a model.
- Sometimes you will have to do something to the variables in order to make the plot a linear function (like squaring both sides of the model).
- The slope of the linear function that fits the data actually means something. Find the slope and find out what it represents (and check it).
- QUOTE: … if you fit a linear equation to that data, what would the slope represent? ...