Improving interval enclosures
نویسنده
چکیده
This paper serves as background information for the Vienna proposal for interval standardization, explaining what is needed in practice to make competent use of the interval arithmetic provided by an implementation of the standard to be. Discussed are methods to improve the quality of interval enclosures of the range of a function over a box, considerations of possible hardware support facilitating the implementation of such methods, and the results of a simple interval challenge that I had posed to the reliable computing mailing list on November 26, 2008. Also given is an example of a bound constrained global optimization problem in 4 variables that has a 2-dimensional continuum of global minimizers. This makes standard branch and bound codes extremely slow, and therefore may serve as a useful degenerate test problem.
منابع مشابه
ON THE SOLUTION OF PARAMETRISEDLINEAR SYSTEMSEvgenija
Considered are parametrised linear systems which parameters are subject to tolerances. Rump's xed-point iteration method for nding outer and inner approximations of the hull of the solution set is studied and applied to an electrical circuit problem. Interval Gauss-Seidel iteration for parametrised linear systems is introduced and used for improving the enclosures, obtained by the xed-point met...
متن کاملThe Automatic Computation of Second-order Slope Tuples for Some Nonsmooth Functions
! , to occur in the function expression of the underlying function. Furthermore, we allow the function expression to contain functions given by two or more branches. By using interval arithmetic, second-order slope tuples provide verified enclosures of the range of the underlying function. We give some examples comparing range enclosures given by a second-order slope tuple with enclosures from ...
متن کاملComputing Enclosures of Overdetermined Interval Linear Systems
This work considers special types of interval linear systems overdetermined systems, systems consisting of more equations than variables. The solution set of an interval linear system is a collection of all solutions of all instances of an interval system. By the instance, we mean a point real system that emerges when we independently choose a real number from each interval coefficient of the i...
متن کاملExponential Enclosure Techniques for the Computation of Guaranteed State Enclosures in ValEncIA-IVP
Verified integration of initial value problems for sets of ordinary differential equations can be performed by numerous approaches. The most important ones are based on either interval or Taylor model arithmetic and enclose with certainty the sets of reachable states at a given point of time. Commonly, such tools are based on a Taylor series expansion of the solution of differential equations i...
متن کاملAn Interval Newton Method Based on the Bernstein Form for Bounding the Zeros of Polynomial Systems
Interval Newton methods are widely used to find reliable enclosures for the roots of the polynomial systems. But the computation process needs the evaluation of an enclosure for the derivative of the polynomial and evaluation of the polynomial at a particular point. Again, the subdivisions (if any are needed) will require repeated evaluation of the function values. We propose an alternative app...
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:
دوره شماره
صفحات -
تاریخ انتشار 2009