Functions of rational Krylov space matrices and their decay properties

Rational Krylov subspaces have become a fundamental ingredient in numerical linear algebra methods associated with reduction strategies. Nonetheless, many structural properties of the reduced matrices in these subspaces are not fully understood. We advance in this analysis by deriving bounds on the entries of rational Krylov reduced matrices and of their functions, that ensure an a-priori decay of their entries as we move away from the main diagonal. As opposed to other decay pattern results in the literature, these properties hold in spite of the lack of any banded structure in the considered matrices. Numerical experiments illustrate the quality of our results

Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices

This paper derives a priori residual-type bounds for the Arnoldi approximation of a matrix function together with a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay behavior of the entries of functions of banded matrices. Specifically, a priori decay bounds for the entries of functions of banded non-Hermitian matrices will be exploited, using Faber polynomial approximation. Numerical experiments illustrate the quality of the results

NEMATODE COOMUNITIES AS INDICATORS OF SOIL QUALITY IN VINEYARD SYSTEM: A CASE OF STUDY IN DEGRADED AREAS

The restoring effect of selective agronomic strategies on optimal soil functionality of degraded areas within organic vineyard was evaluated using the nematode community as an indicator of soil quality. Three different restoring strategies were implemented in two organic farms located in Tuscany (Italy). The relative abundance of nematode trophic groups and the maturity index showed that the use of compost improved soil biological quality and increased the abundance of predators. Instead, dry mulching and green manure applications were useful to control the most dangerous nematodes of grapevines, namely the virus-vector Xiphinema index (Longidoridae)

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

Design Principles for Sparse Matrix Multiplication on the GPU

We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion. While previous SpMM work concentrates on thread-level parallelism, we additionally focus on latency hiding with instruction-level parallelism and load-balancing. We show, both theoretically and experimentally, that the proposed SpMM is a better fit for the GPU than previous approaches. We identify a key memory access pattern that allows efficient access into both input and output matrices that is crucial to getting excellent performance on SpMM. By combining these two ingredients---(i) merge-based load-balancing and (ii) row-major coalesced memory access---we demonstrate a 4.1x peak speedup and a 31.7% geomean speedup over state-of-the-art SpMM implementations on real-world datasets.Comment: 16 pages, 7 figures, International European Conference on Parallel and Distributed Computing (Euro-Par) 201

Motion clouds: model-based stimulus synthesis of natural-like random textures for the study of motion perception

Choosing an appropriate set of stimuli is essential to characterize the response of a sensory system to a particular functional dimension, such as the eye movement following the motion of a visual scene. Here, we describe a framework to generate random texture movies with controlled information content, i.e., Motion Clouds. These stimuli are defined using a generative model that is based on controlled experimental parametrization. We show that Motion Clouds correspond to dense mixing of localized moving gratings with random positions. Their global envelope is similar to natural-like stimulation with an approximate full-field translation corresponding to a retinal slip. We describe the construction of these stimuli mathematically and propose an open-source Python-based implementation. Examples of the use of this framework are shown. We also propose extensions to other modalities such as color vision, touch, and audition

An astrobiological experiment to explore the habitability of tidally locked M-dwarf planets

We present a summary of a three-year academic research proposal drafted during the Sao Paulo Advanced School of Astrobiology (SPASA) to prepare for upcoming observations of tidally locked planets orbiting M-dwarf stars. The primary experimental goal of the suggested research is to expose extremophiles from analogue environments to a modified space simulation chamber reproducing the environmental parameters of a tidally locked planet in the habitable zone of a late-type star. Here we focus on a description of the astronomical analysis used to define the parameters for this climate simulation