A note on unique solvability of the absolute value equation
الموضوعات :
T. Lotfi
1
(Department of Mathematics, Hamedan Branch, Islamic Azad University,
Hamedan, Iran)
H. Vieseh
2
(Department of Mathematics, Hamedan Branch, Islamic Azad University,
Hamedan, Iran)
الکلمات المفتاحية: eigenvalue, Generalized eigenvalue, Quadratic eigenvalue, Iterative method, Numerical computation,
ملخص المقالة :
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 positivedeniteness of a certain point matrix. Special case $B=-I$ is veried too as an application.
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