Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

"Who Fears Death" di Nnedi Okorafor, una proposta di traduzione

This dissertaton deals with the translation of selected chapters from Nnedi Okorafor’s novel Who Fears Death. The novel, set in a post-apocalyptic Africa ravaged by inter-ethnic violence, narrates the tale of Onyesonwu, an Ewu, a half-breed born of rape, facing the rejection of her community. Growing up Onyesonwu realizes that the color of her skin is not the only thing that sets her apart from the other inhabitants of Jwahir, as she starts to manifest magical powers, and during an unintentional visit to the spirit realms she finds out that her biological father, a very powerful sorcerer, wants to kill her. At this point the only option left to her is to learn the secret arts of magic under the guidance of Aro, the sorcerer, and then embark on a journey to put and end to the menace posed by her biological father, stop the massacres between the Okeke and Nuru people, and rewrite history. This work is structured in five chapters. The first presents a brief retelling of the author’s life and works. The second chapter constitutes the theoretical frame according to which the novel will be described, and illustrates an analysis on the function of sci-fi literature. The third chapter introduces the novel itself, dealing with its setting and cultural peculiarities, the literary genre to which it belongs, and analysing the themes deemed most relevant, among which the racial and gender issues. The fourth chapter consists of the translation of some chapters from the novel Who Fears Death, and the fifth of a comment on the translation, presenting both a textual analysis, and notes on the choices deemed most interesting or challenging in a translation process perspective.