A note on unique solvability of the absolute value equation

Subject Areas : Difference and functional equations

T. Lotfi ¹ , H. Vieseh ²

1 - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
2 - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

Received: 2013-01-01 Accepted : 2013-01-01 Published : 2013-06-01

Keywords: eigenvalue, Generalized eigenvalue, Quadratic eigenvalue, Iterative method, Numerical computation,

Abstract :

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 valueequation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability oftheir corresponding absolute value equation. This condition is formulated in terms of positivedeniteness of a certain point matrix. Special case $B=-I$ is veried too as an application.

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