In the eld of computational electrodynamics the discretization of Maxwell's equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extend...

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types minimization problems: a (single) differentiable function and sum non-smooth function. In first case, adopt fixed step size avoid traditional line search establish convergence analysis proposed algorithm quadratic proble...

We discuss the construction of algebraic multilevel preconditioners for the conjugate gradient method and derive explicit and sharp bounds for the convergence rates. We present several numerical examples that demonstrate the efficiency of the preconditioner. sparse approximate inverse, sparse matrix, algebraic multilevel method, preconditioning, conjugate gradient method, Krylov subspace method...

We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a syst...