Medieval conceptions of reason and the modes of thought in Piers Plowman

This thesis is an attempt to shed light on the related questions of how we should read Piers Plowman and of what kind of book its author was trying to write. In the first chapter it is argued that feminine line-endings are an important feature of Langland's metre, and consideration is given to how they affect our reading of the verse. It is suggested that the verse demands a slow and meditative reading, and that Langland's text emerges as a list of items not easily related to each other; the reader is challenged to work out connexions and thus in a sense to compose his own poem. The second chapter is an examination of the medieval conceptions and modes of thought that are associated with the word "reson". The term "reasonable" is later used to refer to these. In the last part of the chapter it is argued that Langland's aim is to make his readers seek salvation, and that he is aware of certain difficulties with the traditional, "reasonable" approaches of other moralists. His own book is "unreasonable"; its mixture of modes of thought, and hence of the thought-worlds they project, makes narrative consistency and definiteness of argument impossible. In the rest of the thesis some of the juxtapositions between modes of thought are examined. The. third chapter deals with "positive” juxtapositions, which create in the reader's mind a sense of satisfying, but nevertheless "unreasonable", illumination; the speech of Wit and the vision of the Passion and Crucifixion are discussed in detail. The fourth chapter deals with "negative" juxtapositions, which provoke a sense of bewilderment and dissatisfaction; discussion centres on Ymaginatiyf's speech in the C text, Need's speech, and the confessions of the Seven Deadly Sins

The Dynamical Functional Particle Method for Multi-Term Linear Matrix Equations

Recent years have seen a renewal of interest in multi-term linear matrix equations, as these have come to play a role in a number of important applications. Here, we consider the solution of such equations by means of the dynamical functional particle method, an iterative technique that relies on the numerical integration of a damped second order dynamical system. We develop a new algorithm for the solution of a large class of these equations, a class that includes, among others, all linear matrix equations with Hermitian positive definite or negative definite coefficients. In numerical experiments, our MATLAB implementation outperforms existing methods for the solution of multi-term Sylvester equations. For the Sylvester equation AX + XB = C, in particular, it can be faster and more accurate than the built-in implementation of the Bartels–Stewart algorithm, when A and B are well conditioned and have very different size

Perturbation bounds for constrained and weighted least squares problems

AbstractWe derive perturbation bounds for the constrained and weighted linear least squares (LS) problems. Both the full rank and rank-deficient cases are considered. The analysis generalizes some results of earlier works

Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges

The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved by benchmarking quantum dynamics of few-body systems against independent exact solutions. A diffusion gauge is implemented here as a so-called noise-matrix, which satisfies a matrix equation defined by the corresponding Fokker--Planck equation of the phase-space representation. For the physical systems with fermionic particles considered here, the numerical evaluation of the new diffusion gauges allows us to double the practical simulation time, compared with hitherto known analytic noise-matrices. This development may have far reaching consequences for future quantum dynamical simulations of many-body systems