Interpolation Flashcards
describes techniques to fit curves to such data to obtain intermediate estimates
Curve Fitting
Computing values of the function at a number of discrete values along the range of interest.
Then, a simpler function may be derived to fit these values.
Curve fitting
Two approaches of curve fitting
least-squares regression
interpolation
where these data exhibit a significant degree of error or “noise,” the strategy is to derive a single
curve that represents the general trend of these data. Because any individual data point may be incorrect, we make no effort to intersect every point. Rather, the curve is designed to follow the pattern of the points taken as a group
least-squares regression
where these data are known to be very precise, the basic approach is to fit a curve or a series of curves that pass directly through each of the points. Such data usually originate from tables.
interpolation
Three attempts to fit a “best” curve through five data points.
Least-squares regression
Linear interpolation
Curvilinear Interpolation
Two types of applications are generally encountered when fitting experimental data
Trend analysis
Hypothesis Testing
represents the process of using the pattern of any data to make predictions.
Trend Analysis
may be used to predict or forecast values of the dependent variable.
Trend Analysis
an existing mathematical model is compared with measured data. If the model coefficients are unknown, it may be necessary to determine values that best fit the observed data. On the other hand, if estimates of the model coefficients are already available, it may be appropriate to compare predicted values of the model with observed values to test the adequacy of the model. Often, alternative models are compared and the “best” one is selected on the basis of empirical observations.
Hypothesis Testing
fittng the “best” straight line through a set of uncertain data points
Linear regression
a general technique for fitting a “best’’ polynomial. Thus, you will learn to derive a parabolic, cubic, or higher-order polynomial that optimally fits uncertain data.
Polynomial regression
It is designed for the case where the dependent variable y is a linear function of two or more independent variables x1, x2, . . . , xm. This approach has special utility for evaluating experimental data where the variable of interest is dependent on a number of different factors
multiple linear regression
an approach designed to compute a least-squares fit of a nonlinear equation to data
nonlinear regression
estimating intermediate values between precise data points
Interpolation
