Bruno Iannazzo

TL;DR: This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars.

TL;DR: An iterative method is presented and analyzed for approximating the Karcher mean of a set of n n positive denite and its values are compared with known values.

TL;DR: Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible singular $M$-matrix, which arises in the study of Markov models, are considered.

TL;DR: The original equation is transformed into an equivalent Riccati equation where the singularity is removed while the matrix coefficients maintain the same structure as in the original equation, leading to a quadratically convergent algorithm with complexity $O(n^2)$ which provides approximations with full precision.

TL;DR: The Barzilai-Borwein method with nonmonotone line-search is shown to be competitive in several Riemannian optimization problems and notably outperforms existing first-order optimization methods.