Does the Best-Fitting Curve Always Exist?

Does the Best-Fitting Curve Always Exist?

In many areas of human practice, one needs to approximate a set of points P1, . . . , Pn ∈ R representing experimental data or observations by a simple geometric shape, such as a line, plane, circular arc, elliptic arc, and spherical surface. This problem is known as fitting amodel object line, circle, sphere, etc. to observed data points. The best fit is achieved when the geometric distances f...

Is the Best Fitting Curve Always Unique?

is is a continuation of our paper [1] where we studied the problem of existence of the best �tting curve. Here we deal with its uniqueness. Our interest in these problems comes from applications where one describes a set of points PP1,... , PPnn (representing experimental data or observations) by simple geometric shapes, such as lines, circular arc, elliptic arc, and so forth. e best �t is ac...

The best parameter subset using the Chebychev curve fitting criterion

Signal detection Using Rational Function Curve Fitting

In this manuscript, we proposed a new scheme in communication signal detection which is respect to the curve shape of received signal and based on the extraction of curve fitting (CF) features. This feature extraction technique is proposed for signal data classification in receiver. The proposed scheme is based on curve fitting and approximation of rational fraction coefficients. For each symbo...

Cannon–thurston Maps Do Not Always Exist

We construct a hyperbolic group with a hyperbolic subgroup for which inclusion does not induce a continuous map of the boundaries. 2010 Mathematics Subject Classification: 20F67