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Showing 1 to 20 of 75 for “"Sparse matrix"”.
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Sparse matrix spaces
… zero, or an arbitrary real number. We call them sparse matrix spaces, abbreviated SMS, and examine under what conditions they contain matrices for which all eigenvalues have strictly negative real parts. We call an SMS with this property stable. We start by reviewing the necessary background from …
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Sparse Matrix Belief Propagation
We propose sparse-matrix belief propagation, which executes loopy belief propagation in Markov random fields by replacing indexing over graph neighborhoods with sparse-matrix operations. This abstraction allows for seamless integration with optimized sparse linear algebra libraries, including those …
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Sparse matrix-vector multiplication by specialization
… in the very common numerical procedure of sparse matrix-vector multiplication, in the case where a single matrix is to be multiplied by many vectors, is explored. The main objective is the evaluation of the speed-ups that can be obtained with program specialization without considering the …
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Structure-based Optimizations for Sparse Matrix-Vector Multiply
… OSF and PBR, to improve the performance of Sparse Matrix-vector Multiply (SMVM) kernels, which dominate the runtime of iterative solvers for systems of linear equations. SMVM computations that use sparse formats typically achieve only a small fraction of peak CPU speeds because they are …
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Optimization by runtime specialization for sparse matrix-vector multiplication
… the potential for obtaining speed-ups for sparse matrix-dense vector multipli- cation using runtime specialization, in the case where a single matrix is to be multiplied by many vectors. We experiment with five methods involving run-time specialization with parallelization, comparing them …
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On implementing sparse matrix-vector multiplication on intel platform
Sparse matrix-vector multiplication, SpMV, can be a performance bottle-neck in iterative solvers and algebraic eigenvalue problems. In this thesis, we present our sparse matrix compressed chunk storage format (CCF) and SpMV CCF kernel that realizes high performance on Intel Xeon multicore and Phi …
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Spatial software pipelining on distributed architectures for sparse matrix codes
… assignment and scheduling techniques for a sparse matrix benchmark, and that spatial software pipelining can improve the execution time of certain loops by over a factor of three.
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Tardigrade: A Hardware Accelerator for Sparse Matrix Multiplication and Sparse Convolution
Sparse matrix-sparse matrix multiplication (SpMSpM) and sparse convolution are critical primitive operations for scientific computing and deep learning. Prior work has proposed accelerators for each of these primitives, but these systems are often specialized to run either SpMSpM or sparse …
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High-Performancs Sparse Matrix-Vector Multiplication on GPUS for Structured Grid Computations
In this thesis, we address efficient sparse matrix-vector multiplication for matrices arising from structured grid problems with high degrees of freedom at each grid node. Sparse matrix-vector multiplication is a critical step in the iterative solution of sparse linear systems of equations arising …
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An investigation into direct sparse matrix solution schemes in the finite element method
… involves the solution of large systems of sparse linear algebraic equations. The solution of these systems often represents a significant or even dominant component of the total solution time. Various sparse matrix techniques and strategies have been developed to reduce the time and cost of …
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The gap between necessity and sufficiency for stability of sparse matrix systems: simulation studies
Sparse matrix systems (SMSs) are potentially very useful for graph analysis and topological representations of interaction and communication among elements within a system. Such systems’ stability can be determined by the Routh-Hurwitz criterion. However, simply using the Routh-Hurwitz criterion is …
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Reducing communication in sparse solvers
Sparse matrix operations dominate the cost of many scientific applications. In parallel, the performance and scalability of these operations is limited by irregular point-to-point communication. Multiple methods are investigated throughout this dissertation for reducing the cost associated with …
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Data parallel algebraic multigrid
Algebraic multigrid methods for large, sparse linear systems are central to many computational simulations. Parallel algorithms for such solvers are generally decomposed into coarse-grain tasks suitable for distributed computers with traditional processing cores. Accelerating multigrid methods on …
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Matrix completion algorithms with applications in biomedicine, e-commerce and social science
This thesis investigates matrix completion algorithms with applications in biomedicine, e-commerce and social science. In general, matrix completion algorithms work well for low rank matrices. Such matrices find many applications in recommender systems and social network analysis. On the other …
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Application of wavelets in few-body problems.
… is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to …
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Analyses of the Lanczos Algorithm and of the Approximation Problem in Richardson's Method
Two algorithms of use in sparse matrix computation are studied. The rounding errors of the computational Lanczos algorithm are examined in order to account for the differences between the ideal and the machine-operator quantities. The observed behavior of these errors is explained by means of a …
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Detection and Decoding: New Learning-Based Algorithms and Their Fundamental Limits
… for practical applications. Second, we propose Sparse Matrix Codes (SMC), a novel channel coding technique tailored for ultra-reliable low-latency communications. SMC maps message bits to a sparse matrix, which is then multiplied by a spreading matrix and transmitted over the communication …
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Matrix Free approach for Raviart-Thomas anisotropic Tensor Product Finite Elements
… thereby extend the existing implementation of matrix free framework in deal.ii. The extensions allow the framework to also support anisotropic vector-valued finite elements in addition to existing isotropic Lagrangian finite elements. Tests on finite element operators in divergence conforming …
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Fill estimation for blocked sparse matrices and tensors
Many sparse matrices and tensors from a variety of applications, such as finite element methods and computational chemistry, have a natural aligned rectangular nonzero block structure. Researchers have designed high-performance blocked sparse operations which can take advantage of this sparse …
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