Formal solution to systems of interval linear or non-linear equations

被引：5
|
作者：
Sainz, Miguel A. [1 ]
Gardeñes, Ernest [2 ]
Jorba, Lambert [3 ]
机构：
[1] Departamento de Informática y Matemática Aplicada, University of Girona, Spain
[2] Departamento de Matemática Aplicada y Análisis, University of Barcelona, Spain
[3] Departamento de Matemática Económica, Financiera y Actuarial, University of Barcelona, Spain
来源：
Reliable Computing | 2002年 / 8卷 / 03期
关键词：
Algorithms - Convergence of numerical methods - Formal logic - Linear equations - Modal analysis - Nonlinear equations - Set theory;
D O I：
10.1023/A:1015561212728
中图分类号：
学科分类号：
摘要：
This is the first of two papers which present the Modal Interval Analysis as a framework where the search and interpretation of formal solutions for a set of simultaneous interval linear or non-linear equations is started on, together with the interval estimations for sets of solutions of real-valued systems in which coefficients and right-hand sides belong to certain intervals. The main purpose of this first paper is to show that the modal intervals are a suitable tool to approach problems where logical references appear. Thus, it is possible to give a logical meaning to general solutions of the system of equations, obtained, in the linear case, by means of an algorithm whose convergence conditions are studied.
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页码：189 / 211
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