Search Results - Computing methodologies → Linear algebra algorithms

Pipirima: Predicting Patterns in Sparsity to Accelerate Matrix Algebra by Bakhtiar, Ubaid, Joo, Donghyeon, Asgari, Bahar

“…While sparsity, a feature of data in many applications, provides optimization opportunities such as reducing unnecessary computations, data transfers, and…”
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ReSMiPS: A ReRAM-based Sparse Mixed-precision Solver with Fast Matrix Reordering Algorithm by Fu, Yuyang, Li, Jiancong, Chen, Jia, Zhou, Zhiwei, Zhou, Houji, Peng, Wenlong, Li, Yi, Miao, Xiangshui

“…The solution of sparse matrix equations is essential in scientific computing. However, traditional solvers on digital computing platforms are limited by memory bottlenecks in largescale sparse matrix storage and computation…”
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SpV8: Pursuing Optimal Vectorization and Regular Computation Pattern in SpMV by Li, Chenyang, Xia, Tian, Zhao, Wenzhe, Zheng, Nanning, Ren, Pengju

“… We evaluate SpV8 on Intel Xeon CPU and compare with multiple state-of-art SpMV algorithms using 71 sparse matrices…”
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FSPA: An FeFET-based Sparse Matrix-Dense Vector Multiplication Accelerator by Zhang, Xiaoyu, Li, Zerun, Liu, Rui, Chen, Xiaoming, Han, Yinhe

“… The performance of traditional SpMV accelerators is bounded by memory. In-memory computing (IMC) is a promising technique to alleviate the memory bottleneck…”
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Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers by Haidar, Azzam, Tomov, Stanimire, Dongarra, Jack, Higham, Nicholas J.

“…Low-precision floating-point arithmetic is a powerful tool for accelerating scientific computing applications, especially those in artificial intelligence…”
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On the Parallel I/O Optimality of Linear Algebra Kernels: Near-Optimal Matrix Factorizations by Kwasniewski, Grzegorz, Kabic, Marko, Ben-Nun, Tal, Ziogas, Alexandros Nikolaos, Saethre, Jens Eirik, Gaillard, Andre, Schneider, Timo, Besta, Maciej, Kozhevnikov, Anton, VandeVondele, Joost, Hoefler, Torsten

“… We first establish a theoretical framework for deriving parallel I/O lower bounds for linear algebra kernels, and then utilize its insights to derive Cholesky and LU schedules, both communicating N^{3}/(P\sqrt{M…”
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Solvability of Matrix-Exponential Equations by Ouaknine, Joel, Pouly, Amaury, Sousa-Pinto, Joao, Worrell, James

“… Our results have applications to reachability problems for linear hybrid automata. Our decidability proof relies on a number of theorems from algebraic and transcendental…”
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Many-Body Electronic Correlation Energy using Krylov Subspace Linear Solvers by Shah, Shikhar, Zhang, Boqin, Huang, Hua, Pask, John E., Suryanarayana, Phanish, Chow, Edmond

“…This paper presents the formulation and implementation of a high performance algorithm to compute the many-body electronic correlation energy via the random-phase approximation within density functional theory…”
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An approximate computing technique for reducing the complexity of a direct-solver for sparse linear systems in real-time video processing by Schaffner, Michael, Gurkaynak, Frank K., Smolic, Aljosa, Kaeslin, Hubert, Benini, Luca

“…Many video processing algorithms are formulated as least-squares problems that result in large, sparse linear systems…”
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Steady-state dynamic temperature analysis and reliability optimization for embedded multiprocessor systems by Ukhov, Ivan, Bao, Min, Eles, Petru, Peng, Zebo

“…In this paper we propose an analytical technique for the steady-state dynamic temperature analysis (SSDTA) of multiprocessor systems with periodic…”
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Hello SME! Generating Fast Matrix Multiplication Kernels Using the Scalable Matrix Extension by Remke, Stefan, Breuer, Alexander

“…Modern central processing units (CPUs) feature single-instruction, multiple-data pipelines to accelerate compute-intensive floating-point and fixed-point…”
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Boosting Graph Spectral Sparsification via Parallel Sparse Approximate Inverse of Cholesky Factor by Chen, Baiyu, Liu, Zhiqiang, Zhang, Yibin, Yu, Wenjian

“…With the advance of very-large-scale-integrated (VLSI) systems, fast and efficient algorithms for solving equations of Laplacian matrices are increasingly significant…”
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GPU Accelerated Sparse Cholesky Factorization by Karsavuran, M. Ozan, Ng, Esmond G., Peyton, Barry W.

“…The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation…”
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High-Performance Eigensolver Combining EigenExa and Iterative Refinement by Uchino, Yuki, Imamura, Toshiyuki

“… Eigenvalue decomposition is ubiquitous in simulations. Various eigensolvers for computing approximations have been developed thus far…”
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Implementing sparse matrix-vector multiplication on throughput-oriented processors by Bell, Nathan, Garland, Michael

“…Sparse matrix-vector multiplication (SpMV) is of singular importance in sparse linear algebra…”
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COPA: Constrained PARAFAC2 for Sparse & Large Datasets by Afshar, Ardavan, Perros, Ioakeim, Papalexakis, Evangelos E, Searles, Elizabeth, Ho, Joyce, Sun, Jimeng

“…PARAFAC2 has demonstrated success in modeling irregular tensors, where the tensor dimensions vary across one of the modes. An example scenario is modeling…”
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Scaling lattice QCD beyond 100 GPUs by Babich, R., Clark, M. A., Joó, B., Shi, G., Brower, R. C., Gottlieb, S.

“…Over the past five years, graphics processing units (GPUs) have had a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations…”
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Geometry-oblivious FMM for compressing dense SPD matrices by Yu, Chenhan D., Levitt, James, Reiz, Severin, Biros, George

“…We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, or "compression," of an arbitrary dense symmetric…”
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On monte carlo hybrid methods for linear algebra by Dávila, Diego, Alexandrov, Vassil, Esquivel-Flores, Oscar A.

“…This paper presents an enhanced hybrid (e.g. stochastic/ deterministic) method for Linear Algebra based on bulding an efficient stochastic preconditioner and then solving the corresponding System of Linear Algebraic Equations (SLAE…”
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Combining Models and Guided Empirical Search to Optimize for Multiple Levels of the Memory Hierarchy by Chen, Chun, Chame, Jacqueline, Hall, Mary

“…This paper describes an algorithm for simultaneously optimizing across multiple levels of the memory hierarchy for dense-matrix computations…”
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