Is the Best Fitting Curve Always Unique?

نویسندگان

  • N. Chernov
  • Q. Huang
چکیده

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 achieved when the geometric distances from the given points to the �tting curve are minimized, in the least squares sense. Finding the best �t reduces to the minimization of the objective function

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Application of Discounted Residual Income for Capital Assets Pricing by Method Curve Fitting with Sinusoidal Functions

The basic model for valuation of firm is the Dividend Discount Model (DDM). When investors buy stocks, they expect to receive two types of cash flow: dividend in the period during which the stock is owned, and the expected sales price at the end of the period. In the extreme example, the investor keeps the stock until the company is liquidated; in such a case, the liquidating dividend becomes t...

متن کامل

Capturing Outlines of Planar Generic Images by Simultaneous Curve Fitting and Sub-division

In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data points. A maximum error has been determined to preserve the absolute fitting error less than a criterion and it administers the process of curv...

متن کامل

Real and Generic Data without Unconstrained Best-Fitting Verhulst Curves and Sufficient Conditions for Median Mitscherlich and Verhulst Curves to Exist

A commonly taught scientific method for building mathematical models uses finite computations to approximate the curve of a specified type that best fits the data, without checking whether any such best-fitting curve exists: not every regression objective need have a global unconstrained minimum. One counterexample will confute its theoretical foundation: any triple of points with super-exponen...

متن کامل

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...

متن کامل

Fitting Martingales To Given Marginals

We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant mean. We show that, under the extra condition that they are weakly continuous, the marginals can always be fitted in a unique way by a martingale which lies in a particular class of strong Markov pro...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012