Contractivity of linear fractional transformations
نویسنده
چکیده
One possible approach to exact real arithmetic is to use linear fractional transformations (LFT's) to represent real numbers and computations on real numbers. Recursive expressions built from LFT's are only convergent (i.e., denote a well-deened real number) if the involved LFT's are suuciently contractive. In this paper, we deene a notion of contrac-tivity for LFT's. It is used for convergence theorems and for the analysis and improvement of algorithms for elementary functions.
منابع مشابه
Integrating Goal Programming, Taylor Series, Kuhn-Tucker Conditions, and Penalty Function Approaches to Solve Linear Fractional Bi-level Programming Problems
In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent...
متن کاملDefining relations of a group $Gamma= G^{3,4}(2,Z)$ and its action on real quadratic field
In this paper, we have shown that the coset diagrams for the action of a linear-fractional group $Gamma$ generated by the linear-fractional transformations $r:zrightarrow frac{z-1}{z}$ and $s:zrightarrow frac{-1}{2(z+1)}$ on the rational projective line is connected and transitive. By using coset diagrams, we have shown that $r^{3}=s^{4}=1$ are defining relations for $Gamma$. Furt...
متن کاملOn the Contractivity and Convergence of General Linear Methods on Semi-Infinite Intervals
The strict-contractivity and the convergence of General Linear Methods on the classes of strictly dissipative and dissipative differential systems regarding some inner product are analyzed. New convergence and contractivity results of the methods on semi-infinite intervals are provided for the case of strictly dissipative problems. Some applications of the main results to the class of Runge-Kut...
متن کاملFractional Darboux Transformations
In this paper we utilize the covariance of Riccati equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of fractional Darboux transformations which can be recognized also as generalized Cole-Hopf transformations. We apply these transformations to find Schrodinger equations...
متن کاملOn the convergence of fractal transforms
This paper reports on investigations concerning the convergence of fractal transforms for signal modelling. Convergence is essential for the functionality of fractal based coding schemes. The coding process is described as non-linear transformation in the finite-dimensional vector space. Using spectral theory, a necessary and sufficient condition for the contractivity is derived from the eigenv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Theor. Comput. Sci.
دوره 279 شماره
صفحات -
تاریخ انتشار 2002