Beschreibung:
<jats:p>Recent works on the multilinear system<jats:inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><mi mathvariant="script">A</mi><msup><mrow><mi mathvariant="bold">x</mi></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mi mathvariant="bold">b</mi></math></jats:inline-formula>with an order-<jats:inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"><mi>m</mi></math></jats:inline-formula>and dimension-<jats:inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"><mi>n</mi></math></jats:inline-formula>tensor<jats:inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"><mi mathvariant="script">A</mi></math></jats:inline-formula>and a vector<jats:inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"><mi mathvariant="bold">b</mi></math></jats:inline-formula>of dimension-<jats:inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"><mi>n</mi></math></jats:inline-formula>have been motivated by their applications in data mining, numerical PDEs, tensor complementary problems, and so on. In this paper, we propose an alternating minimization method for the solution of the system mentioned above and present several randomized versions of this algorithm in order to improve its performance. The provided numerical experiments show that our methods are feasible for any tensor<jats:inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"><mi mathvariant="script">A</mi></math></jats:inline-formula>and outperform some existing ones in the same case.</jats:p>