Parallel implementation of the matrix rank test for randomness assessment

2014 ◽  
Author(s):  
Kinga Marton ◽  
Vlad Baja ◽  
Alin Suciu
Keyword(s):  
Parallel Implementation ◽  
Rank Test ◽  
Matrix Rank ◽  
The Matrix ◽  
Test For Randomness

scholarly journals Calculating the Energy Spectrum of Complex Low-Dimensional Heterostructures in the Electric Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Svetlana N. Khonina ◽  
Sergey G. Volotovsky ◽  
Sergey I. Kharitonov ◽  
Nikolay L. Kazanskiy
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Ground State ◽  
State Energy ◽  
Airy Functions ◽  
Piecewise Constant ◽  
Matrix Rank ◽  
The Matrix ◽  
Constant Potential ◽  
Low Dimensional

An algorithm for solving the steady-state Schrödinger equation for a complex piecewise-constant potential in the presence of theE-field is developed and implemented. The algorithm is based on the consecutive matching of solutions given by the Airy functions at the band boundaries with the matrix rank increasing by no more than two orders, which enables the characteristic solution to be obtained in the convenient form for search of the roots. The algorithm developed allows valid solutions to be obtained for the electric field magnitudes larger than the ground-state energy level, that is, when the perturbation method is not suitable.

Multiply Separated Synthesis of Six-Link Mechanisms Using Parallel Homotopy With M-Homogenization

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
M. Zhang
Keyword(s):  
Group Theory ◽  
Matrix Method ◽  
Parallel Implementation ◽  
Homotopy Methods ◽  
Numerical Work ◽  
Function Generation ◽  
Connection Machine ◽  
The Matrix ◽  
Generation Problem ◽  
Complete Solutions

Abstract This paper presents complete solutions to the function generation problem of six-link Watt and Stephenson mechanisms, with multiply separated precision positions (PP), using homotopy methods with m-homogenization. It is seen that using the matrix method for synthesis, applying m-homogeneous group theory and by defining auxiliary equations in addition to the synthesis equations, the number of homotopy paths to be tracked in obtaining all possible solutions to the synthesis problem can be drastically reduced. Numerical work dealing with the synthesis of Watt and Stephenson mechanisms for 6 and 9 multiply separated precision points is presented. For both mechanisms, it is seen that complete solutions for 6 and 9 precision points can be obtained by tracking 640 and 286,720 paths, respectively. A parallel implementation of homotopy methods on the Connection Machine on which several thousand homotopy paths can be tracked concurrently is also discussed.

scholarly journals Comparison of Three Recent Personalization Algorithms

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Matrix Factorization ◽  
Parallel Implementation ◽  
Apache Spark ◽  
Test Set ◽  
Hit Rate ◽  
The Matrix ◽  
Bayesian Personalized Ranking ◽  
Personalized Ranking

<p>Personalization algorithms recommend products to users based on their previous interactions with the system. The products could be books, movies, or products in a retail system. The earliest personalization algorithms were based on factorization of the user-item matrix where each entry in the matrix would correspond to an interaction, or absence of an interaction of the user with the product. In this article, we compare three recently developed personalization algorithms. The three algorithms are Bayesian Personalized Ranking, Taxonomy Discovery for Personalized Recommendations and Multi-Matrix Factorization. We compare the three algorithms on the hit rate @ position 10 on a held out test set on 1 million users and 200 thousand items in the catalog of Target Corporation. We report our findings in table 1. We develop all three algorithms on an Apache Spark parallel implementation.</p>

Calculation of the Magnetization of Permanent Magnets, Based on the Method for Solving the Inverse Problem Using Parallel Calculations

2021 ◽  
Vol 64 (1) ◽  
pp. 13-21
Author(s):  
Petr Denisov ◽  
◽  
Anna Balaban ◽  
Keyword(s):  
Inverse Problem ◽  
Permanent Magnets ◽  
Parallel Implementation ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Tikhonov Regularization Method ◽  
Field Pattern ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
The Matrix

The article proposes the modification of a technique for assessing the magnetization of permanent magnets from the known field pattern. The identification method is based on solving an ill-conditioned system of linear algebraic equations by the Tikhonov regularization method. The method of boundary integral equations based on scalar potentials is used to compile the matrix of coefficients. The article presents the algorithm that uses parallel computations when performing the most time-consuming operations to reduce the time for solving the inverse problem. In order to check the proposed method, a program was developed that allows to simulate the measurement process: to calculate the direct problem and find the magnetic induction at the points of the air gap, then introduce the error into the "measurement results" and solve the inverse problem. The results of nu-merical experiments that allow us to evaluate the advantages of parallel implementation using the capabilities of modern multi-core processors are presented.

ON DESIGNING COMMUNICATION-INTENSIVE ALGORITHMS FOR A SPANNING OPTICAL BUS BASED ARRAY

1995 ◽  
Vol 05 (03) ◽  
pp. 499-511 ◽  
Author(s):  
CHUNMING QIAO
Keyword(s):  
Parallel Algorithms ◽  
Parallel Implementation ◽  
Reconfigurable Array ◽  
The Matrix ◽  
Matrix Transposition ◽  
Optical Buses ◽  
And Control

The Reconfigurable Array with Spanning Optical Buses (or RASOB) architecture provides flexible reconfiguration and strong connectivities with low hardware and control complexities. We use a parallel implementation of the matrix transposition as well as multiplication algorithms as an example to show how the architectural capabilities can be taken advantage of in designing efficient parallel algorithms.

scholarly journals On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product

2004 ◽  
Vol 2004 (58) ◽  
pp. 3103-3116 ◽  
Author(s):  
Yongge Tian
Keyword(s):  
Mixed Type ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Reverse Order ◽  
Matrix Product ◽  
Matrix Rank ◽  
Matrix Rank Method ◽  
The Matrix ◽  
Necessary And Sufficient

Some mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product are established. Necessary and sufficient conditions for these laws to hold are found by the matrix rank method. Some applications and extensions of these reverse-order laws to the weighted Moore-Penrose inverse are also given.

scholarly journals The Computational Complexity of Some Problems of Linear Algebra

1996 ◽  
Vol 3 (33) ◽  
Author(s):  
Jonathan F. Buss ◽  
Gudmund Skovbjerg Frandsen ◽  
Jeffery O. Shallit
Keyword(s):  
Computational Complexity ◽  
Commutative Ring ◽  
Linear Algebra ◽  
Polynomial Time ◽  
Matrix Rank ◽  
Maximum Rank ◽  
The Matrix ◽  
Np Complete

We consider the computational complexity of some problems dealing with matrix rank.<br /> Let E, S be subsets of a commutative ring R.<br />Let x1, x2, ..., xt be variables. Given a matrix M = M(x1, x2, ..., xt)<br />with entries chosen from E union {x1, x2, ..., xt}, we want to determine<br />maxrankS(M) = max rank M(a1, a2, ... , at)<br />and<br />minrankS(M) = min rank M(a1, a2, ..., at). <br />There are also variants of these problems that specify more about the<br />structure of M, or instead of asking for the minimum or maximum rank, <br />ask if there is some substitution of the variables that makes the matrix<br /> invertible or noninvertible.<br />Depending on E, S, and on which variant is studied, the complexity<br />of these problems can range from polynomial-time solvable to random<br />polynomial-time solvable to NP-complete to PSPACE-solvable to<br />unsolvable.

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