Curve Fitting Techniques FinalReport (original) (raw)

Curve and Surface Fitting Using The Least Square Approximation with Applications

Koya University, 2015

In this project, we studied the least square method. Which is one of the more popular methods to represent a collected data that are used for predicting the future of life problems. The study contains three chapters, the first one involve introduction to this method and some basic definition that we were using it in the project. The chapter two is talk about the task of this method in start then studied the formula of least square method and some basic of their derivatives where others state in appendix chapter, with addition of estimating the error and choosing best fit, multivariate polynomial approximation of the least square method, then in the last chapter, it is applications chapter like the way for convert the non-linear least square curves had been discussed such as the exponential, growth rate, polynomials and other special curves into the linear least square curves or linearizing each one of them, time series and Fourier approximation with sinusoidal and application of the surface fitting are fixed.

Algorithm 716: TSPACK: tension spline curve-fitting package

ACM Transactions on Mathematical Software, 1993

The primary purpose of TSPACK is to construct a smooth function which interpolates a discrete set of data points. The function may be required to have either one or two continuous derivatives. If the accuracy of the data does not warrant interpolation, a smoothing function (which does not pass through the data points) may be constructed instead. The fitting method is designed to avoid extraneous inflection points (associated with rapidly varying data values) and preserve local shape properties of the data (monotonicity and convexity), or to satisfy the more general constraints of bounds on function values or first derivatives. The package also provides a parametric representation for construction general planar curves and space curves.