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Topic: Curve fitting

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	Curve Fitting
		Curve fits to data with linear constraints on the fit parameters.
		In curve fitting we have raw data and a function with unknown coefficients.
		This is a point on the surface where the coefficient values of the fitting function minimize, in the least-squares sense, the difference between the experimental data and fit data (the model).
	www.wavemetrics.com /products/igorpro/dataanalysis/curvefitting.htm (743 words)

	Curve-fitting
		Curve fitting has two steps: First select a family of curves, then find the best fitting curve by some statistical criterion such as the method of least squares (e.g.
		Curve fitting may be used to determine the best fitting member of the family, thereby effecting a measurement the theoretical parameter, nk.
		The simplicity of a family of curves is measured by the paucity of parameters.
	philosophy.wisc.edu /forster/curve-fitting.htm (750 words)

	Curve Fitting Sample - Math and Statistics Library for C# and VB.NET: BLAS, LAPACK, more
		Curve fitting is the process of finding the curve that best approximates a set of points from within a set of curves.
		Curve classes come with methods to evaluate the function, its derivative and integral, and to find the roots or zeroes of a curve.
		Curve fitting is the process of finding the curve that best approximates a set of points from within a set of curves which are linear combinations of a set of basis functions.
	www.extremeoptimization.com /mathematics/Samples/CurveFitting.aspx (1547 words)

	Research Topics - IP curve fitting
		Classical least squares fitting of IP curves is the most straightforward approach to this problem: the error function is the sum of squared values of the polynomial at the points in the data set.
		The IP curve is not an adequate representation for the data because it has several pieces and does not respect the continuity of the data curve it is fitted to.
		Consequently, the IP curve (shown on top of the surface with the fl curve) is broken into several pieces as the gradient of the polynomial along the data set switches back and forth between pointing towards the outside of the data curve and the inside.
	www.lems.brown.edu /~tt/2Dfitting/ipcurves.html (1578 words)

	Curve Fitting - QuB
		Curve fitting is available for all histograms and Results#Select charts, and the high-res pane of the Data and Data Overlap windows.
		After you fit, errors are estimated using the square root of the diagonal of the approximate curvature matrix.
		The curve persists after you close the dialog, until you zoom on a different stretch of data or choose "Clear fit curve".
	www.qub.buffalo.edu /wiki/index.php/Curve_Fitting (1382 words)

	Curve fitting - Wikipedia, the free encyclopedia
		Curve fitting is finding a curve which matches a series of data points and possibly other constraints.
		This section is an introduction to both interpolation (where an exact fit to constraints is expected) and curve fitting/regression analysis (where an approximate fit is permitted).
		This may not happen with high-order polynomial curves, they may even have values that are very large in positive or negative magnitude.
	en.wikipedia.org /wiki/Curve_fitting (1095 words)

	Curve Fitting
		The basic idea of the fits is to take a list of functions that you specify, and try to find a linear combination of them which approximates your data as well as possible.
		Another common use of fits is in finding approximate formulas to describe a particular set of data.
		This uses the polynomial fit to extrapolate the data.
	documents.wolfram.com /v4/MainBook/3.8.1.html (537 words)

	Curve Fitting
		There are general approaches for curve fitting that are distinguished from each other on the basis of the amount of error associated with the data.
		Second, where the data is known to be very precise, the basic approach is to fit a curve of a series of curves that pass directly through each of the points.
		In case of the polynomial curve types, one of the least-squares method, you are allowed to select a curve order of from 1 through 10, and for the Fourier series curve type, you can choose the order of from 1 through 100.
	www.mathpad.com /public/htmls/main/left/fit/CurveFitInfo.html (491 words)

	Interactive Curve Fitting :: Getting Started (Curve Fitting Toolbox)
		You use New Fit at the beginning of your curve fitting session, and when you are exploring different fit types for a given data set.
		The fit and residuals for the single-term exponential equation indicate it is a poor fit overall.
		Because the goal of fitting the census data is to extrapolate the best fit to predict future population values, you should explore the behavior of the fits up to the year 2050.
	www.mathworks.com /access/helpdesk/help/toolbox/curvefit/bquz7v5.html (2140 words)

	Curve Fitting
		Curve fitting is finding a line or curve that passes most closely through a given set of points, minimizing the distances between the line and the actual points and providing the function whose curve is the line.
		When a set of points is used, a new measurement showing the curve will be added and the function and settings will be appended as a comment.
		Nevertheless, when calculating a Curve fitting measurement, normal Cartesian coordinates are used in all cases, so graphics coordinates are counted from the bottom left corner of the image.
	bersoft.com /bimagem/help/best_fit_line.htm (877 words)

	Curve fitting made easy - The Industrial Physicist
		The goal of data (or curve) fitting is to find the parameter values that most closely match the data.
		This function depends on the method used to do the fitting, and the function is typically chosen as the sum of the squares of the vertical deviations from each data point to the curve.
		The prediction interval is represented by two curves lying on opposite sides of the fitted curve.
	www.tipmagazine.com /tip/INPHFA/vol-9/iss-2/p24.html (2314 words)

	Intro. to Signal Processing:Curve fitting
		The objective of curve fitting is to find a mathematical equation that describes the signal and that is minimally influenced by the presence of noise.
		This is a linear equation that can be fit by the least squares method in order to estimate a and b (but only approximately, because the log transformation effects the weighting of the errors due to random noise).
		The best fit equation, shown by the green solid line in the figure, is Y = 0.9897 exp(- 0.98896 X), that is a = 0.9897 and b = -0.98896, very close to the expected values.
	www.wam.umd.edu /~toh/spectrum/CurveFitting.html (694 words)

	Logistic Curve Fitting
		Since L is the "limiting population" for the "S" shaped logistic curve, a value of L that is appropriate to the problem at hand can usually be obtained by guessing.
		Use the method of "data linearization" to find the logistic curve that fits the data for the population of the U.S. for the years 1900-1990.
		Various curves can be fit, but they all depend on the value of L. No one knows this value in advance and it must be estimated.
	math.fullerton.edu /mathews/n2003/LogisticEquationMod.html (202 words)

	Curve Fit/X Curve Fitting Example Software - Cubic Spline BSplines
		Curve Fit/X is both an ActiveX Control and a COM object, implemented in a single DLL, yet it can be used in a wide range of programming languages that support these standards.
		This method enables the usual cubic spline model to be extended to the case where, instead of fitting a spline model through all data points (knots), which could result in a very "wriggly" curve, allows a smooth curve to be fit to the data.
		Curve Fit/X will pass the data back in an array indexed from the value you specify in a property of the control.
	windale.com /curvefitx.php (935 words)

	Fitting a curve without choosing a model
		Your approach to curve fitting depends on your goal.
		Lowess curves can be helpful when the data progresses monotonically, but are less helpful when there are peaks or valleys.
		The fine curve reveals the fine structure of the data, but tends to wiggle a lot.
	www.graphpad.com /curvefit/other_curve_fits_.htm (457 words)

	curve fitting (Site not responding. Last check: 2007-11-01)
		Curve fitting is an important and useful technique for handling data because it produces a mathematical model of the data that can compactly contain and represent its primary properties.
		This is based on the idea that a line is positioned so that the algebraic sum of the differences between the observed and calculated values of the ordinates (the residuals) is equal to zero.
		The most common type of curve fitting involves fitting a straight line to an aggregate of data.
	www.vuse.vanderbilt.edu:8888 /es130/lectures/lecture6/curvefitnew.html (828 words)

	Graphs and Curve Fitting (Site not responding. Last check: 2007-11-01)
		If a smooth curve is drawn through such a plot of points it may give some idea of the curve that expresses the functional relationship between the variables.
		Drawing a smooth curve or a straight line on a graph is a useful but rather subjective procedure.
		To do this the idea is to form some measure of how closely a line fits the data and find the values of the slope and intercept which optimize this measure.
	teacher.nsrl.rochester.edu /phy_labs/AppendixC/AppendixC.html (1910 words)

	Getting Started with the Curve Fitting Toolbox (Curve Fitting Toolbox)
		The curve fitting session is defined as the current collection of fits for all data sets.
		If you have many data sets to fit and you want to automate the fitting process, you should use the Curve Fitting Tool to select the appropriate model and fit options, generate an M-file, and then run the M-file in batch mode.
		Fit options such as whether the data should be normalized, the fit starting points, and the fitting method
	www.weizmann.ac.il /matlab/toolbox/curvefit/ch_star8.html (613 words)

	Curve Fitting
		Curve fitting is the process of finding various ways to fit a curve to a series of data points which best represents all points.
		Curve fitting model - used to select the type of model used to try to fit a curve to the data.
		The new curve created by the curve fitting operation is added to the Data Manager.
	www.astro.princeton.edu /~esirko/idl_html_help/it_plots12.html (271 words)

	eFunda: Exponential Curve Fitting
		This calculator finds the least-squares fit to a list of tow-column data as a exponential function with polynomial exponent up to a specified order.
		The size of input data is limited to 1024 points or less to converve system resources.
		Fit above data using exponential function with polynomial exponents
	www.efunda.com /webM/numerical/curvefitexp.cfm (150 words)

	Curve Software: LAB Fit Curve Fitting Software, Curve Pilot for Mac, FindGraph, DataFit, NLREG, ...
		Curve fitting fit nonlinear regression treatment of data basic statistics error propagation 2D and 3D graphs confidence ba...
		DataFit is a tool for performing curve fitting statistical analysis data plotting Fit equations with up to 100 parameters...
		NLREG performs nonlinear regression and curve fitting NLREG fits a mathematical function whose form you specify to a set o...
	www.windfile.com /find/curve (340 words)

	DataFit Curve Fitting and Data Plotting Software by Oakdale Engineering (Site not responding. Last check: 2007-11-01)
		The philosophy at Oakdale Engineering is that the simplicity of the curve fitting process is just as important as achieving accurate results.
		Curve fitting is now easier to perform than ever.
		DataFitX version 2.0 is a COM component (in-process DLL) that allows you to perform nonlinear curve fitting or cubic spline interpolation from within your program with only a few simple lines of code.
	www.curvefitting.com /index.html (281 words)

	Curve Fitting (Site not responding. Last check: 2007-11-01)
		Nonlinear regression, also known as curve fitting, nicely integrates statistics and the study of functions.
		And if in the study of polynomials, exponential or log functions or periodic functions students in your classroom are working with real problems containing real data (and I hope they are) then there is no choice about including this topic.
		The paper Curve Fitting, available as a Word 2 document only, discusses the mathematics needed to understand nonlinear regression.
	exploringdata.cqu.edu.au /curv_fit.htm (318 words)

	Scientific Computing FAQ: Curve Fitting, Data Modelling, Interpolation, Extrapolation (Site not responding. Last check: 2007-11-01)
		ODRPACK, from Netlib, is a portable collection of Fortran subprograms for fitting a model to data.
		ODRPACK from Netlib (see Netlib) is an excellent library for a production mode approach to fitting these data, with a graphical user interface at Plato Guide At the very beginning of the User's Guide there is a description of how to fit data to an ellipse or circle.
		Gaussfit is a superb response to the whole family of problems of adjusting parameters to fit functions to data; it is especially effective and easy to use for one-time problems and for exploratory work [Don Wells].
	www.mathcom.com /corpdir/techinfo.mdir/scifaq/q230.html (2609 words)

	Chi-Square Curve Fitting
		The "smooth curve" is a curve that mostly passes through the error bars (which have a size denoted by
		On average a good fit will have as many unusually large deviations as unusually small deviations, that is, on average the ratio of deviation to error will be about 1.
		Clearly it is a useless process to fit a curve exactly through inexact data.
	www.physics.csbsju.edu /stats/chi_fit.html (2318 words)

	TableCurve 2D: automated curve fitting and equation discovery, distributed by NET Engineering
		And, unlike most curve fitting programs, TableCurve 2D's user-defined functions are compiled so custom curve fitting can be performed quickly -- at nearly the speed as with the built-in equations.
		Once your XY data have been fit, TableCurve automatically sorts and plots the fitted equations by the statistical criteria you select (r2, DOF adjusted r2, Fit Standard Error or the F Statistic).
		Many researchers spend hours and even weeks to discover the ideal model that describes their data.This is because they use tools that require trial and error curve fitting.
	www.net-eng.it /eng/products/tablecurve2d/tablecurve2.html (2096 words)

	IDL Curve Fitting and Function Optimization
		The F distribution is used in testing ratios of variances and for addition of parameters in chi square fitting.
		The function MPFITELLIPSE is used to fit an elliptical shape to a set of X-Y scatter points.
		MPFIT is still recommended for curve fitting applications, but TNMIN will be useful when general minimization is desired.
	cow.physics.wisc.edu /~craigm/idl/fitting.html (632 words)

	Module Adds Curve-Fitting and Optimization Capabilities to the HP-71B
		Fitting OBSERVED DATA to a mathematical model and finding the optimum values for a multivariable function are common engineering needs.
		The Curve Fit Pac's powerful curve-fitting capabilities are based on a minimization algorithm known as the Fletcher-Powell method.
		For example, consider the case where a curve is being fit with a user-written model that has three parameters and does not compute the gradient.
	www.hpmuseum.org /journals/71curve.htm (2473 words)

	DataFit Curve Fitting and Data Plotting Software by Oakdale Engineering
		The philosophy at Oakdale Engineering is that the simplicity of the curve fitting process is just as important as achieving accurate results.
		Curve fitting is now easier to perform than ever.
		DataFitX version 2.0 is a COM component (in-process DLL) that allows you to perform nonlinear curve fitting or cubic spline interpolation from within your program with only a few simple lines of code.
	www.curvefitting.com (281 words)

	Tutorial: 1D Curve Fitting in IDL using MPFITFUN and MPFITEXPR
		Furthermore, the IDL supplied curve fitting routine, called CURVEFIT, is not as robust as I would like.
		By fitting a curve to your data, you are assuming that a particular model best represents the data.
		All of the fitting procedures here also allow you to impose lower and upper bounding constraints on any combination of the parameters you choose.
	cow.physics.wisc.edu /~craigm/idl/mpfittut.html (1667 words)

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