Algebraic Solving of Complex Interval Linear Systems by Limiting ‎Factors‎

A new idea for exact solving of the complex interval linear systems

In this paper‎, ‎the aim is to find a complex interval vector [Z] such that satisfies the complex interval linear system C[Z]=[W]‎. ‎For this‎, ‎we present a new method by restricting the general solution set via applying some parameters‎. ‎The numerical examples are given to show ability and reliability of the proposed method.

Estimation of algebraic solution by limiting the solution set of an interval linear system

In this paper, we introduce a new method for estimating the algebraic solution of an interval linear system (ILS) whose coefficient matrix is real-valued and righthand side vector is interval-valued. In the proposed method, we first apply the interval Gaussian elimination procedure to obtain the solution set of an interval linear system and then by limiting the solution set of related ILS by th...

Complex fuzzy linear systems

Discovering Non-linear Ranking Functions by Solving Semi-algebraic Systems

Differing from [6] this paper reduces non-linear ranking function discovering for polynomial programs to semi-algebraic system solving, and demonstrates how to apply the symbolic computation tools, DISCOVERER and QEPCAD, to some interesting examples. keywords: Program Verification, Loop Termination, Ranking Function, Polynomial Programs, Semi-Algebraic Systems, Computer Algebra, DISCOVERER, QEPCAD

Dynamical systems method for solving ill-conditioned linear algebraic systems

A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is ju...

Interval Methods and Condition Numbers of Linear Algebraic Systems

The sensitivity of linear systems is often expressed in terms of condition numbers, e.g., the ordinary, the effective, or the local condition number, all of which are computed via singular value decomposition. We express the sensitivity of linear systems by using interval methods, and by means of experiments using three particularly suitable systems we indicate which condition numbers are relev...