A Graph Approach to Observability in Physical Sparse Linear Systems

A sparse linear system constitutes a valid model for a broad range of physical systems, such as electric power networks, industrial processes, control systems or traffic models. The physical magnitudes in those systems may be directly measured by means of sensor networks that, in conjunction with data obtained from contextual and boundary constraints, allow the estimation of the state of the systems. The term observability refers to the capability of estimating the state variables of a system based on the available information. In the case of linear systems, diffierent graphical approaches were developed to address this issue. In this paper a new unified graph based technique is proposed in order to determine the observability of a sparse linear physical system or, at least, a system that can be linearized after a first order derivative, using a given sensor set. A network associated to a linear equation system is introduced, which allows addressing and solving three related problems: the characterization of those cases for which algebraic and topological observability analysis return contradictory results; the characterization of a necessary and sufficient condition for topological observability; the determination of the maximum observable subsystem in case of unobservability. Two examples illustrate the developed techniques

Using postordering and static symbolic factorization for parallel sparse LU

Theme 1 - Reseaux et systemes - Projet RESEDASSIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 F, issue : a.2000 n.237 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Using postordering and static symbolic factorization for parallel sparse LU

In this paper we present several improvements of widely used parallel LU factorization methods on sparse matrices. First we introduce the LU elimination forest and then we characterize the L, U factors in terms of their corresponding LU elimination forest. This characterization can be used as a compact storage scheme of the matrix as well as of the task dependence graph. To improve the use of BLAS in the numerical factorization, we perform a postorder traversal of the LU elimination forest, thus obtaining larger supernodes. To expose more task parallelism for a sparse matrix, we build a more accurate task dependence graph that includes only the least necessary dependences. Experiments compared favorably our methods against methods implemented in the S * environment on the SGI’s Origin2000 multiprocessor. 1. Introduction an