Generalized Fractional Algebraic Linear System Solvers

This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that finding x solution $$\sum _{\alpha \in \mathbb {R}}A^{\alpha }x=b$$ . These will be referred as Generalized Fractional Algebraic Linear Systems (GFALS). In this paper, we derive gradient methods for solving these very computationally complex problems, which themselves require intermiediate standard (FALS) $$A^{\alpha , with $$\alpha {R_+}$$ The latter usually many classical $$Ax=b$$ We also show in some cases, a GFALS problem can obtained first-order hyperbolic system conservation laws. discuss connections between PDE-approach and gradient-type methods. convergence analysis addressed experiments are proposed illustrate compare paper.