A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems
نویسندگان
چکیده
Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals providing better algebraic properties. In particular, the generalized interval arithmetic is a group for addition and for multiplication of zero free intervals. These properties allow one constructing a LU decomposition of a generalized interval matrix A: the two computed generalized interval matrices L and U satisfy A = LU with equality instead of the weaker inclusion obtained in the context of classical intervals. Some potential applications of this generalized interval LU decomposition are investigated.
منابع مشابه
Algebraic Solving of Complex Interval Linear Systems by Limiting Factors
In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...
متن کاملA 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.
متن کاملAnalytical and Verified Numerical Results Concerning Interval Continuous-time Algebraic Riccati Equations
This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...
متن کاملGeneralized H-differentiability for solving second order linear fuzzy differential equations
In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...
متن کاملSolutions of Fuzzy Linear Systems using Ranking function
In this work, we propose an approach for computing the compromised solution of an LR fuzzy linear system by using of a ranking function when the coefficient matrix is a crisp mn matrix. To do this, we use expected interval to find an LR fuzzy vector, X , such that the vector (AX ) has the least distance from (b) in 1 norm and the 1 cut of X satisfies the crisp linear system AX = b ...
متن کامل