The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, networks and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificially-generated matrices cannot meet, and is widely used by the sparse matrix algorithms community for the development and performance evaluation of sparse matrix algorithms. The collection includes software for accessing and managing the collection, from MATLAB, Fortran, and C.

We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. To perform most of the numerical computation in dense matrix kernels, we introduce the notion of unsymmetric supernodes. To better exploit the memory hierarchy, weintroduce unsymmetric supernode-panel updates and two-dimensional data partitioning. To speed up symbolic factorization, we use Gilbert and Peierls's depth- rst search with Eisenstat and Liu's symmetric structural reductions. We have implemented a sparse LU code using all these ideas. We present experiments demonstrating that it is signi cantly faster than earlier partial pivoting codes. We also compare performance with Umfpack, which uses a multifrontal approach; our code is usually faster.

This paper discusses computational experiments with linear optimization problems involving semidefinite, quadratic, and linear cone constraints (SQLPs). Many test problems of this type are solved using a new release of SDPT3, a Matlab implementation of infeasible primal-dual path-following algorithms. The software developed by the authors uses Mehrotratype predictor-corrector variants of interior-point methods and two types of search directions: the HKM and NT directions. A discussion of implementation details is provided and computational results on problems from the SDPLIB and DIMACS Challenge collections are reported.

Getting good I/O performance from parallel programs is a critical problem for many application domains. In this paper, we report our experience tuning the I/O performance of four application programs from the areas of satellite-data processing and linear algebra. After tuning, three of the four applications achieve application-level I/O rates of over 100 MB/s on 16 processors. The total volume of I/O required by the programs ranged from about 75 MB to over 200 GB. We report the lessons learned in achieving high I/O performance from these applications, including the need for code restructuring, local disks on every node and knowledge of future I/O requests. We also report our experience on achieving high performance on peer-to-peer configurations. Finally, we comment on the necessity of complex I/O interfaces like collective I/O and strided requests to achieve high performance. 1 Introduction I/O has been identified as one of the major obstacles to achieving high performance from para...

Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matrix entries on the diagonal. Complete block diagonal supernode pivoting allows dynamical interchanges of columns and rows during the factorization process. The level-3 BLAS efficiency is retained and an advanced two-level left–right looking scheduling scheme results in good speedup on SMP machines. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications. Key words: Computational sciences, numerical linear algebra, direct solver, unsymmetric linear systems

Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasi-Newton approximations are made. The performance of the code is studied using a set of difficult test problems from the CUTE collection.

This dissertation presents new techniques for solving large sparse unsymmetric linear systems on high performance computers, using Gaussian elimination with partial pivoting. The efficiencies of the new algorithms are demonstrated for matrices from various fields and for a variety of high performance machines. In the first part we discuss optimizations of a sequential algorithm to exploit the memory hierarchies that exist in most RISC-based superscalar computers. We begin with the left-looking supernode-column algorithm by Eisenstat, Gilbert and Liu, which includes Eisenstat and Liu's symmetric structural reduction for fast symbolic factorization. Our key contribution is to develop both numeric and symbolic schemes to perform supernodepanel updates to achieve better data reuse in cache and floating-point register...

Interpolation of a spatially correlated random process is used in many areas. The best unbiased linear predictor, often called kriging predictor in geostatistical science, requires the solution of a large linear system based on the covariance matrix of the observations. In this article, we show that tapering the correct covariance matrix with an appropriate compactly supported covariance function reduces the computational burden significantly and still has an asymptotic optimal mean squared error. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms. Extensive Monte Carlo simulations support the theoretical results. An application to a large climatological precipitation dataset is presented as a concrete practical illustration.

We describe the code PCx, a primal-dual interior-point code for linear programming. Information is given about problem formulation and the underlying algorithm, along with instructions for installing, invoking, and using the code. Computational results on standard test problems are tabulated. The current version number is 1.0. Key words: linear programming, interior-point methods, software. 1 This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W-31-109Eng -38. 1 Introduction PCx is a linear programming solver developed at the Optimization Technology Center at Argonne National Laboratory and Northwestern University. It implements a variant of Mehrotra's predictor-corrector algorithm [6] with the higher-order correction strategy of Gondzio [3]. This primal-dual approach has proved to be the most efficient interior-point method for gene...

. We investigate a modified Cholesky algorithm typical of those used in most interiorpoint codes for linear programming. Cholesky-based interior-point codes are popular for three reasons: their implementation requires only minimal changes to standard sparse Cholesky algorithms (allowing us to take full advantage of software written by specialists in that area); they tend to be more efficient than competing approaches that use alternative factorizations; and they perform robustly on most practical problems, yielding good interior-point steps even when the coefficient matrix of the main linear system to be solved for the step components is ill-conditioned. We investigate this surprisingly robust performance by using analytical tools from matrix perturbation theory and error analysis, illustrating our results with computational experiments. Finally, we point out the potential limitations of this approach. Key words. interior-point algorithms and software, Cholesky factorization, matrix p...