On the unique solution of the generalized absolute value equation
نویسندگان
چکیده
منابع مشابه
A note on unique solvability of the absolute value equation
It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...
متن کاملOn unique solvability of the absolute value equation
It is proved that applying sufficient regularity conditions to the interval matrix [A − |B|, A + |B|], we can create a new unique solvability condition for the absolute value equation Ax + B|x| = b, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive definiteness of a certain point mat...
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One of the issues that has been considered by the researchers in terms of theory and practice is the problem of finding minimum norm solution. In fact, in general, absolute value equation may have infinitely many solutions. In such cases, the best and most natural choice is the solution with the minimum norm. In this paper, the minimum norm-1 solution of absolute value equation is investigated. ...
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15 صفحه اولAbsolute value equation solution via dual complementarity
By utilizing a dual complementarity condition, we propose an iterative method for solving the NPhard absolute value equation (AVE): Ax−|x| = b, where A is an n×n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving a succession of linear programs. The algorithm was tested on 500 consecutively generated random solvable instances of the AVE w...
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ژورنال
عنوان ژورنال: Optimization Letters
سال: 2020
ISSN: 1862-4472,1862-4480
DOI: 10.1007/s11590-020-01672-2