Curve Fitting Application of numerical techniques in science and engineering often involve curve fitting of experimental data. In science and engineering it is often the case that an experiment produces a set of data points (x),...(xNN),where the abscissas {x are distinct.If all the numerical values {x),v}are known to several significant digits of accuracy,then polynomial interpolation can be used successfully;otherwise,it cannot. However,many experiments are done with equipment that is reliable only to three or fewer digits of accuracy.Often,there is an experimental error in the measurements. How do we find the best approximation that goes near(not always through)the points?Curve Fitting ◼ Application of numerical techniques in science and engineering often involve curve fitting of experimental data. ◼ In science and engineering it is often the case that an experiment produces a set of data points (x1 ,y1 ),…,(xN,yN), where the abscissas {xk} are distinct. If all the numerical values {xk}, {yk} are known to several significant digits of accuracy, then polynomial interpolation can be used successfully; otherwise, it cannot. ◼ However, many experiments are done with equipment that is reliable only to three or fewer digits of accuracy. Often, there is an experimental error in the measurements. ◼ How do we find the best approximation that goes near (not always through) the points?