scholarly journals AN APPROXIMATE MATRIX INVERSION PROCEDURE BY PARALLELIZATION OF THE SHERMAN–MORRISON FORMULA

2009 ◽  
Vol 51 (1) ◽  
pp. 1-9 ◽  
Author(s):  
KENTARO MORIYA ◽  
LINJIE ZHANG ◽  
TAKASHI NODERA
Keyword(s):  
Matrix Factorization ◽  
Computational Time ◽  
Approximate Inverse ◽  
Linear System Of Equations ◽  
Processing Elements ◽  
The Matrix ◽  
Large Linear System ◽  
Inversion Procedure ◽  
Parallel Technique ◽  
Better Than

AbstractThe Sherman–Morrison formula is one scheme for computing the approximate inverse preconditioner of a large linear system of equations. However, parallelizing a preconditioning approach is not straightforward as it is necessary to include a sequential process in the matrix factorization. In this paper, we propose a formula that improves the performance of the Sherman–Morrison preconditioner by partially parallelizing the matrix factorization. This study shows that our parallel technique implemented on a PC cluster system of eight processing elements significantly reduces the computational time for the matrix factorization compared with the time taken by a single processor. Our study has also verified that the Sherman–Morrison preconditioner performs better than ILU or MR preconditioners.

scholarly journals Collaborative Filtering Recommendation Using Nonnegative Matrix Factorization in GPU-Accelerated Spark Platform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Bing Tang ◽  
Linyao Kang ◽  
Li Zhang ◽  
Feiyan Guo ◽  
Haiwu He
Keyword(s):  
Collaborative Filtering ◽  
Processing Speed ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Experimental Results ◽  
Computational Time ◽  
Data Sets ◽  
Heterogeneous Cluster ◽  
The Matrix

Nonnegative matrix factorization (NMF) has been introduced as an efficient way to reduce the complexity of data compression and its capability of extracting highly interpretable parts from data sets, and it has also been applied to various fields, such as recommendations, image analysis, and text clustering. However, as the size of the matrix increases, the processing speed of nonnegative matrix factorization is very slow. To solve this problem, this paper proposes a parallel algorithm based on GPU for NMF in Spark platform, which makes full use of the advantages of in-memory computation mode and GPU acceleration. The new GPU-accelerated NMF on Spark platform is evaluated in a 4-node Spark heterogeneous cluster using Google Compute Engine by configuring each node a NVIDIA K80 CUDA device, and experimental results indicate that it is competitive in terms of computational time against the existing solutions on a variety of matrix orders. Furthermore, a GPU-accelerated NMF-based parallel collaborative filtering (CF) algorithm is also proposed, utilizing the advantages of data dimensionality reduction and feature extraction of NMF, as well as the multicore parallel computing mode of CUDA. Using real MovieLens data sets, experimental results have shown that the parallelization of NMF-based collaborative filtering on Spark platform effectively outperforms traditional user-based and item-based CF with a higher processing speed and higher recommendation accuracy.

scholarly journals A Neural Network-Inspired Matrix Formulation of Chemical Kinetics for Acceleration on GPUs

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2710
Author(s):  
Shivam Barwey ◽  
Venkat Raman
Keyword(s):  
Neural Network ◽  
Chemical Kinetics ◽  
Graphics Processing Units ◽  
Source Term ◽  
Turbulent Flames ◽  
Peak Performance ◽  
Computational Time ◽  
Detailed Chemical Kinetics ◽  
The Matrix ◽  
Artificial Neural

High-fidelity simulations of turbulent flames are computationally expensive when using detailed chemical kinetics. For practical fuels and flow configurations, chemical kinetics can account for the vast majority of the computational time due to the highly non-linear nature of multi-step chemistry mechanisms and the inherent stiffness of combustion chemistry. While reducing this cost has been a key focus area in combustion modeling, the recent growth in graphics processing units (GPUs) that offer very fast arithmetic processing, combined with the development of highly optimized libraries for artificial neural networks used in machine learning, provides a unique pathway for acceleration. The goal of this paper is to recast Arrhenius kinetics as a neural network using matrix-based formulations. Unlike ANNs that rely on data, this formulation does not require training and exactly represents the chemistry mechanism. More specifically, connections between the exact matrix equations for kinetics and traditional artificial neural network layers are used to enable the usage of GPU-optimized linear algebra libraries without the need for modeling. Regarding GPU performance, speedup and saturation behaviors are assessed for several chemical mechanisms of varying complexity. The performance analysis is based on trends for absolute compute times and throughput for the various arithmetic operations encountered during the source term computation. The goals are ultimately to provide insights into how the source term calculations scale with the reaction mechanism complexity, which types of reactions benefit the GPU formulations most, and how to exploit the matrix-based formulations to provide optimal speedup for large mechanisms by using sparsity properties. Overall, the GPU performance for the species source term evaluations reveals many informative trends with regards to the effect of cell number on device saturation and speedup. Most importantly, it is shown that the matrix-based method enables highly efficient GPU performance across the board, achieving near-peak performance in saturated regimes.

scholarly journals Green–Haar wavelets method for generalized fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mujeeb ur Rehman ◽  
Dumitru Baleanu ◽  
Jehad Alzabut ◽  
Muhammad Ismail ◽  
Umer Saeed
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Computational Time ◽  
Operational Matrices ◽  
Numerical Techniques ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems ◽  
Better Than

Abstract The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with the classical Haar wavelets technique. In the context of error analysis, an upper bound for error is established to show the convergence of the method. Results of numerical experiments have been documented in a tabular and graphical format to elaborate the accuracy and efficiency of addressed methods. Further, we conclude that accuracy-wise Green–Haar approach is better than the conventional Haar wavelets approach as it takes less computational time compared to the Haar wavelet method.

Arithmetic of matrices over rings

2021 ◽  
Author(s):  
V.P. Shchedryk ◽  
Keyword(s):  
Graduate Students ◽  
Normal Form ◽  
Matrix Factorization ◽  
Ring Theory ◽  
Stable Range ◽  
Matrix Rings ◽  
Principal Ideals ◽  
Factorization Theory ◽  
Close Relationship ◽  
The Matrix

The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals do- mains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a close relationship between the matrix factorization and specific properties of subgroups of the complete linear group and the special normal form of matrices with respect to unilateral equivalence. The properties of matrices over rings of stable range 1.5 are thoroughly studied. The book is intended for experts in the ring theory and linear algebra, senior and post-graduate students.

Martin Shapiro: An Appreciation

The Forum ◽  
2016 ◽  
Vol 14 (2) ◽  
Author(s):  
R. Shep Melnick
Keyword(s):  
Institutional Environment ◽  
Empirical Studies ◽  
The Political ◽  
Public Officials ◽  
Thick Description ◽  
Past Half Century ◽  
The Us ◽  
The Matrix ◽  
The One ◽  
Better Than

AbstractOver the past half century no judicial politics scholar has been more respected or influential than Martin Shapiro. Yet it is hard to identify a school of thought one could call “Shapiroism.” Rather than offer convenient methodologies or grand theories, Shapiro provides rich empirical studies that show us how to think about the relationship between law and courts on the one hand and politics and governing on the other. Three key themes run through Shapiro’s impressive oevre. First, rather than study courts in isolation, political scientists should view them as “one government agency among many,” and seek to “integrate the judicial system in the matrix of government and politics in which it actually operates.” Law professors may understand legal doctrines better than political scientists, but we know (or should know) the rest of the political system better than they do. Second, although judges inevitably make political decisions, their institutional environment leads them to act differently from other public officials. Most importantly, their legitimacy rests on their perceived impartiality within the plaintiff-defendant-judge triad. The conflict between judges’ role as impartial arbiter and enforcer of the laws of the regime can never be completely resolved and places powerful constraints on their actions. Third, the best way to understand the complex relationship between courts and other elements of the regime is comparative analysis. Shapiro played a major role in resuscitating comparative law, especially in his work comparing the US and the EU. All this he did with a rare combination of thick description and crisp, jargon-free analysis, certainly a rarity the political science of our time.

scholarly journals Lossless Linear Integer signal Resampling

2012 ◽  
pp. 225-233
Author(s):  
S.Raghavendra Prasad ◽  
Dr.P.Ramana Reddy
Keyword(s):  
Matrix Factorization ◽  
High Frequency ◽  
Irreversible Process ◽  
Polynomial Interpolation ◽  
Factorization Method ◽  
Special Cases ◽  
The Matrix ◽  
Frequency Components ◽  
Linear Transform ◽  
Signal Resampling

This paper describes about signal resampling based on polynomial interpolation is reversible for all types of signals, i.e., the original signal can be reconstructed losslessly from the resampled data. This paper also discusses Matrix factorization method for reversible uniform shifted resampling and uniform scaled and shifted resampling. Generally, signal resampling is considered to be irreversible process except in some special cases because of strong attenuation of high frequency components. The matrix factorization method is actually a new way to compute linear transform. The factorization yields three elementary integer-reversible matrices. This method is actually a lossless integer-reversible implementation of linear transform. Some examples of lower order resampling solutions are also presented in this paper.

scholarly journals ANALISA PERBANDINGAN METODE SIMULATED ANNEALING DAN LARGE NEIGHBORHOOD SEARCH UNTUK MEMECAHKAN MASALAH LOKASI DAN RUTE KENDARAAN DUA ESELON

2020 ◽  
Vol 4 (1) ◽  
pp. 35-46
Author(s):  
Winarno (Universitas Singaperbangsa Karawang) ◽  
A. A. N. Perwira Redi (Universitas Pertamina)
Keyword(s):  
Simulated Annealing ◽  
Computational Time ◽  
Neighborhood Search ◽  
Large Neighborhood Search ◽  
Location Routing Problem ◽  
Routing Problem ◽  
Large Neighborhood ◽  
Location Routing ◽  
Node Removal ◽  
Better Than

AbstractTwo-echelon location routing problem (2E-LRP) is a problem that considers distribution problem in a two-level / echelon transport system. The first echelon considers trips from a main depot to a set of selected satellite. The second echelon considers routes to serve customers from the selected satellite. This study proposes two metaheuristics algorithms to solve 2E-LRP: Simulated Annealing (SA) and Large Neighborhood Search (LNS) heuristics. The neighborhood / operator moves of both algorithms are modified specifically to solve 2E-LRP. The proposed SA uses swap, insert, and reverse operators. Meanwhile the proposed LNS uses four destructive operator (random route removal, worst removal, route removal, related node removal, not related node removal) and two constructive operator (greedy insertion and modived greedy insertion). Previously known dataset is used to test the performance of the both algorithms. Numerical experiment results show that SA performs better than LNS. The objective function value for SA and LNS are 176.125 and 181.478, respectively. Besides, the average computational time of SA and LNS are 119.02s and 352.17s, respectively.AbstrakPermasalahan penentuan lokasi fasilitas sekaligus rute kendaraan dengan mempertimbangkan sistem transportasi dua eselon juga dikenal dengan two-echelon location routing problem (2E-LRP) atau masalah lokasi dan rute kendaraan dua eselon (MLRKDE). Pada eselon pertama keputusan yang perlu diambil adalah penentuan lokasi fasilitas (diistilahkan satelit) dan rute kendaraan dari depo ke lokasi satelit terpilih. Pada eselon kedua dilakukan penentuan rute kendaraan dari satelit ke masing-masing pelanggan mempertimbangan jumlah permintaan dan kapasitas kendaraan. Dalam penelitian ini dikembangkan dua algoritma metaheuristik yaitu Simulated Annealing (SA) dan Large Neighborhood Search (LNS). Operator yang digunakan kedua algoritma tersebut didesain khusus untuk permasalahan MLRKDE. Algoritma SA menggunakan operator swap, insert, dan reverse. Algoritma LNS menggunakan operator perusakan (random route removal, worst removal, route removal, related node removal, dan not related node removal) dan perbaikan (greedy insertion dan modified greedy insertion). Benchmark data dari penelitian sebelumnya digunakan untuk menguji performa kedua algoritma tersebut. Hasil eksperimen menunjukkan bahwa performa algoritma SA lebih baik daripada LNS. Rata-rata nilai fungsi objektif dari SA dan LNS adalah 176.125 dan 181.478. Waktu rata-rata komputasi algoritma SA and LNS pada permasalahan ini adalah 119.02 dan 352.17 detik.

Machinability and Microstructure of SiC/h-BN Nano-Composites

2008 ◽  
Vol 569 ◽  
pp. 45-48
Author(s):  
Hai Yun Jin ◽  
Guan Jun Qiao ◽  
Zong Ren Peng ◽  
Ji Qiang Gao
Keyword(s):  
Fracture Strength ◽  
Nano Composites ◽  
Weak Interface ◽  
X Ray Diffraction ◽  
X Ray ◽  
Sic Particles ◽  
N2 Atmosphere ◽  
The Matrix ◽  
Better Than

SiC particles coated with nano-BN were synthesized and the machinable SiC/BN ceramic nano-composites were fabricated by Plasma Active Sintering (PAS) in N2 atmosphere. The existing and distribution of h-BN phase were revealed by X-ray diffraction (XRD), and SEM. For the existing of weak interface between h-BN and SiC grains, the machinability of both SiC/BN micro-composites and nano-composites were improved obviously. Because the nano-sized h-BN crystals were homogeneously dispersed around the SiC grains of the matrix, the fracture strength of the nano-composites was better than the SiC/h-BN micro-composite.

scholarly journals Infrared Non-Destructive Testing via Semi-Nonnegative Matrix Factorization

Proceedings ◽  
2019 ◽  
Vol 27 (1) ◽  
pp. 13 ◽  
Author(s):  
Yousefi ◽  
Ibarra-Castanedo ◽  
Maldague
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix ◽  
Principal Component ◽  
Computational Time ◽  
Detection Accuracy ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Non Destructive ◽  
Non Negative Matrix Factorization ◽  
Subsurface Defects

Detection of subsurface defects is undeniably a growing subfield of infrared non-destructive testing (IR-NDT). There are many algorithms used for this purpose, where non-negative matrix factorization (NMF) is considered to be an interesting alternative to principal component analysis (PCA) by having no negative basis in matrix decomposition. Here, an application of Semi non-negative matrix factorization (Semi-NMF) in IR-NDT is presented to determine the subsurface defects of an Aluminum plate specimen through active thermographic method. To benchmark, the defect detection accuracy and computational load of the Semi-NMF approach is compared to state-of-the-art thermography processing approaches such as: principal component thermography (PCT), Candid Covariance-Free Incremental Principal Component Thermography (CCIPCT), Sparse PCT, Sparse NMF and standard NMF with gradient descend (GD) and non-negative least square (NNLS). The results show 86% accuracy for 27.5s computational time for SemiNMF, which conclusively indicate the promising performance of the approach in the field of IR-NDT.

scholarly journals Differentiating isoform functions with collaborative matrix factorization

2019 ◽  
Author(s):  
Keyao Wang ◽  
Jun Wang ◽  
Carlotta Domeniconi ◽  
Xiangliang Zhang ◽  
Guoxian Yu
Keyword(s):  
Matrix Factorization ◽  
Characteristic Curve ◽  
Function Prediction ◽  
Low Rank ◽  
Data Matrix ◽  
Supplementary Information ◽  
Genomic Databases ◽  
Gene Level ◽  
The Matrix ◽  
Level Function

Abstract Motivation Isoforms are alternatively spliced mRNAs of genes. They can be translated into different functional proteoforms, and thus greatly increase the functional diversity of protein variants (or proteoforms). Differentiating the functions of isoforms (or proteoforms) helps understanding the underlying pathology of various complex diseases at a deeper granularity. Since existing functional genomic databases uniformly record the annotations at the gene-level, and rarely record the annotations at the isoform-level, differentiating isoform functions is more challenging than the traditional gene-level function prediction. Results Several approaches have been proposed to differentiate the functions of isoforms. They generally follow the multi-instance learning paradigm by viewing each gene as a bag and the spliced isoforms as its instances, and push functions of bags onto instances. These approaches implicitly assume the collected annotations of genes are complete and only integrate multiple RNA-seq datasets. As such, they have compromised performance. We propose a data integrative solution (called DisoFun) to Differentiate isoform Functions with collaborative matrix factorization. DisoFun assumes the functional annotations of genes are aggregated from those of key isoforms. It collaboratively factorizes the isoform data matrix and gene-term data matrix (storing Gene Ontology (GO) annotations of genes) into low-rank matrices to simultaneously explore the latent key isoforms, and achieve function prediction by aggregating predictions to their originating genes. In addition, it leverages the PPI network and GO structure to further coordinate the matrix factorization. Extensive experimental results show that DisoFun improves the AUROC (area under the receiver-operating characteristic curve) and AUPRC (area under the precision-recall curve) of existing solutions by at least 7.7% and 28.9%, respectively. We further investigate DisoFun on four exemplar genes (LMNA, ADAM15, BCL2L1, and CFLAR) with known functions at the isoform-level, and observed that DisoFun can differentiate functions of their isoforms with 90.5% accuracy. Availability The code of DisoFun is available at mlda.swu.edu.cn/codes.php?name=DisoFun. Supplementary information Supplementary data are available at Bioinformatics online.

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