Kyle A. Gallivan

Strategies for cache and local memory management by global program transformation

Abstract In this paper we describe a method for using data dependence analysis to estimate cache and local memory demand in highly iterative scientific codes. The estimates take the form of a family of “reference” windows for each variable that reflects the current set of elements that should be kept in cache. It is shown that, in important special cases, we can estimate the size of the window and predict a lower bound on the number of cache hits. If the machine has local memory or cache that can be managed by the compiler, these estimates can be used to guide the management of this resource. It is also shown that these estimates can be used to guide program transformations in an attempt to optimize cache performance.

The gSOAP Toolkit for Web Services and Peer-to-Peer Computing Networks

This paper presents the gSOAP stub and skeleton compiler. The compiler provides a unique SOAP-to-C/C++ language binding for deploying C/C++ applications in SOAP Web Services, clients, and peer-to-peer computing networks. gSOAP enables the integratation of (legacy) C/C++/Fortran codes, embedded systems, and real-time software in Web Services, clients, and peers that share computational resources and information with other SOAP-enabled applications, possibly across different platforms, language environments, and disparate organizations located behind firewalls. Results on interoperability, legacy code integration, scalability, and performance are given.

Trust-Region Methods on Riemannian Manifolds

A general scheme for trust-region methods on Riemannian manifolds is proposed and analyzed. Among the various approaches available to (approximately) solve the trust-region subproblems, particular attention is paid to the truncated conjugate-gradient technique. The method is illustrated on problems from numerical linear algebra.

Asymptotic waveform evaluation via a Lanczos method

In this paper we show that the two-sided Lanczos procedure combined with implicit restarts, offers significant advantages over Pade approximations used typically for model reduction in circuit simulation.

A rational Lanczos algorithm for model reduction

This paper presents a model reduction method for large-scale linear systems that is based on a Lanczos-type approach. A variant of the nonsymmetric Lanczos method, rational Lanczos, is shown to yield a rational interpolant (multi-point Padé approximant) for the large-scale system. An exact expression for the error in the interpolant is derived. Examples are utilized to demonstrate that the rational Lanczos method provides opportunities for significant improvements in the rate of convergence over single-point Lanczos approaches.

Parallel algorithms for dense linear algebra computations

Scientific and engineering research is becoming increasingly dependent upon the development and implementation of efficient parallel algorithms on modern high-performance computers. Numerical linear algebra is an indispensable tool in such research and this paper attempts to collect and describe a selection of some of its more important parallel algorithms. The purpose is to review the current status and to provide an overall perspective of parallel algorithms for solving dense, banded, or block-structured problems arising in the major areas of direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers. A major emphasis is given here to certain computational primitives whose efficient execution on parallel and vector computers is essential in order to obtain high performance algorithms.

Impact of Hierarchical Memory Systems On Linear Algebra Algorithm Design

Linear algebra algorithms based on the BLAS or ex tended BLAS do not achieve high performance on mul tivector processors with a hierarchical memory system because of a lack of data locality. For such machines, block linear algebra algorithms must be implemented in terms of matrix-matrix primitives (BLAS3). Designing ef ficient linear algebra algorithms for these architectures requires analysis of the behavior of the matrix-matrix primitives and the resulting block algorithms as a func tion of certain system parameters. The analysis must identify the limits of performance improvement possible via blocking and any contradictory trends that require trade-off consideration. We propose a methodology that facilitates such an analysis and use it to analyze the per formance of the BLAS3 primitives used in block methods. A similar analysis of the block size-perfor mance relationship is also performed at the algorithm level for block versions of the LU decomposition and the Gram-Schmidt orthogonalization procedures.

Model Reduction of MIMO Systems via Tangential Interpolation

In this paper, we address the problem of constructing a reduced order system of minimal McMillan degree that satisfies a set of tangential interpolation conditions with respect to the original system under some mild conditions. The resulting reduced order transfer function appears to be generically unique and we present a simple and efficient technique to construct this interpolating reduced order system. This is a generalization of the multipoint Pade technique which is particularly suited to handle multiinput multioutput systems.

Optimal linear representations of images for object recognition

Although linear representations are frequently used in image analysis, their performances are seldom optimal in specific applications. This paper proposes a stochastic gradient algorithm for finding optimal linear representations of images for use in appearance-based object recognition. Using the nearest neighbor classifier, a recognition performance function is specified and linear representations that maximize this performance are sought. For solving this optimization problem on a Grassmann manifold, a stochastic gradient algorithm utilizing intrinsic flows is introduced. Several experimental results are presented to demonstrate this algorithm.

H2-optimal model reduction of MIMO systems

We consider the problem of approximating a p × m rational transfer function H(s) of high degree by another p × m rational transfer function bH(s) of much smaller degree. We derive the gradients of the H2-norm of the approximation error and show how stationary points can be described via tangential interpolation.