Adaptive matrix algebras in unconstrained minimization
Linear Algebra and its Applications, vol. 471, pp. 544–568, 2015
In this paper we study adaptive $L(k)QN$ methods, involving special matrix algebras of low complexity, to solve general (non-structured) unconstrained minimization problems. These methods, which generalize the classical BFGS method, are based on an iterative formula which exploits, at each step, an ad hoc chosen matrix …
A preconditioning approach to the PageRank computation problem
Linear Algebra and its Applications, vol. 435, pp. 2222–2246, 2011
Some spectral properties of the transition matrix of an oriented graph indicate the preconditioning of Euler-Richardson (ER) iterative scheme as a good way to compute efficiently the vertexrank vector associated with such graph. We choose the preconditioner from an algebra $\mathcal U$ of matrices, thereby obtaining an …