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1st International Conference on Technologies for Smart Green Connected Society 2021, ICTSGS 2021

作者： Ganesh, R. Velu, C.M. SaveethaUniversity Tamil Nadu Chennai602105 India

ISBN: (纸本)9781607685395

The framework has been made for a Movie Rating System to enable us to enjoy our time fruitfully. Film recommendation systems enable users to sort and select the best film fans to see without going through thousands of films which were stored in archives. A total of 392 samples were collected from movie datasets available in kaggle. For this two algorithms were used, one matrix decomposition algorithm and another Support Vector Regression(SVR) algorithm, both the algorithms were executed and compared for accuracy. SVR achieved accuracy, precision, sensitivity and specificity of 87%, 88%, 89% and 93% respectively compared to 80%, 83%, 84% and 86% by the matrix decomposition algorithm. The results were obtained with a level of significance with (p © The Electrochemical Society

关键词： Artificial Intelligence Machine Learning matrix decomposition algorithm Peculiar recommendation Popularity SVR algorithm

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Multi-level method of fundamental solutions for solving polyharmonic problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 456卷

作者： Karageorghis, Andreas Chen, C. S. Univ Cyprus Dept Math & Stat POB 20537 CY-1678 Nicosia Cyprus Univ Southern Mississippi Sch Math & Nat Sci Hattiesburg MS 39406 USA

We consider a multi-level method of fundamental solutions for solving polyharmonic problems governed by 4N N u = 0 , N is an element of N\{1} in both two and three dimensions. Instead of approximating the solution with linear combinations of N fundamental solutions, we show that, with appropriate deployments of the source points, it is possible to employ an approximation involving only the fundamental solution of the operator 4N N . To determine the optimal position of the source points, we apply the recently developed effective condition number method. In addition, we show that when the proposed technique is applied to boundary value problems in circular or axisymmetric domains, with appropriate distributions of boundary and source points, it lends itself to the application of matrix decomposition algorithms. The results of several numerical tests are presented and analysed.

关键词： Polyharmonic equation Effective condition number matrix decomposition algorithm Method of fundamental solutions

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A fourth-order orthogonal spline collocation method for two-dimensional Helmholtz problems with interfaces

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NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2020年第6期36卷 1811-1829页

作者： Bhal, Santosh Kumar Danumjaya, Palla Fairweather, Graeme BITS Goa Campus Dept Math Pilani 403726 Goa India Amer Math Soc Math Reviews Ann Arbor MI USA

Orthogonal spline collocation is implemented for the numerical solution of two-dimensional Helmholtz problems with discontinuous coefficients in the unit square. A matrix decomposition algorithm is used to solve the collocation matrix system at a cost ofO(N-2 log N)on anN x Npartition of the unit square. The results of numerical experiments demonstrate the efficacy of this approach, exhibiting optimal global estimates in various norms and superconvergence phenomena for a broad spectrum of wave numbers.

关键词： almost block diagonal linear systems discontinuous data fast Fourier transforms Helmholtz problems matrix decomposition algorithm optimal global convergence rates orthogonal spline collocation superconvergence

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Orthogonal Spline Collocation Methods for Fluid Flow Problems

Orthogonal Spline Collocation Methods for Fluid Flow Problem...

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作者： Fisher, Nicholas Llewellyn Colorado School of Mines

学位级别：Ph.D.

We propose an approach for the numerical solution of the Navier-Stokes equations based on a pressure Poisson equation reformulation. Through an alternating direction implicit extrapolated Crank--Nicolson time discretization, the scheme decouples the updates for velocity and pressure terms. Moreover, the proposed scheme reduces the Navier-Stokes equations to a Burgers' equation for the velocity terms and a singular Neumann Poisson equation for the pressure. These two sub-problems are analyzed in turn. We use extrapolated alternating direction implicit Crank-Nicolson orthogonal spline collocation with splines of order r to solve the coupled Burgers' equations in two space variabl and two unknown functions. The scheme is initialized with an alternating direction implicit predictor-corrector method. We show theoretically that the H1 norm of the error at each time level is of order r in space and of order 2 in time. Then we use a matrix decomposition algorithm for the orthogonal spline collocation solution to Poisson's equation with Neumann boundary conditions. We show theoretically that the H1 semi-norm of the error is of order r. In each case, our numerical results confirm these theoretical orders. Finally, the combined scheme is implemented for the solution of the pressure Poisson reformulation of the Navier--Stokes equations using splines of equal order. Numerical results show that the scheme obtains the expected optimal order convergence rates for both the velocity and pressure terms.

关键词： Burgers' equation Navier-Stokes equations Poisson's equation matrix decomposition algorithm Alternating direction implicit Orthogonal spline collocation

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A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients

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NUMERICAL algorithmS 2018年第2期77卷 491-516页

作者： Bialecki, Bernard Karageorghis, Andreas Colorado Sch Mines Dept Appl Math & Stat Golden CO 80401 USA Univ Cyprus Dept Math & Stat POB 20537 CY-1678 Nicosia Cyprus

We solve the Dirichlet and mixed Dirichlet-Neumann boundary value problems for the variable coefficient Cauchy-Navier equations of elasticity in a square using a Legendre spectral Galerkin method. The resulting linear system is solved by the preconditioned conjugate gradient (PCG) method with a preconditioner which is shown to be spectrally equivalent to the matrix of the resulting linear system. Numerical tests demonstrating the convergence properties of the scheme and PCG are presented.

关键词： Cauchy-Navier equations Legendre polynomials Spectral methods matrix decomposition algorithm Preconditioned conjugate gradient method

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The plane waves method for axisymmetric Helmholtz problems

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2016年 69卷 46-56页

作者： Karageorghis, Andreas Univ Cyprus Dept Math & Stat POB 20537 CY-1678 Nicosia Cyprus

The plane waves method is employed for the solution of Dirichlet and Neumann boundary value problems for the homogeneous Helmholtz equation in two- and three-dimensional domains possessing radial symmetry. The appropriate selection of collocation points and unitary direction vectors in the method leads to circulant and block circulant coefficient matrices in two and three dimensions, respectively. We propose efficient matrix decomposition algorithms which make use of fast Fourier transforms for the solution of the systems resulting from such a discretization. In conjunction with the method of particular solutions, the method is extended to the solution of inhomogeneous axisymmetric Helmholtz problems. Several numerical examples are presented. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Plane waves method Collocation matrix decomposition algorithm Fast Fourier transforms Helmholtz equation

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Finite Difference Schemes for the Cauchy-Navier Equations of Elasticity with Variable Coefficients

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JOURNAL OF SCIENTIFIC COMPUTING 2015年第1期62卷 78-121页

作者： Bialecki, Bernard Karageorghis, Andreas Colorado Sch Mines Dept Appl Math & Stat Golden CO 80401 USA Univ Cyprus Dept Math & Stat CY-1678 Nicosia Cyprus

We solve the variable coefficient Cauchy-Navier equations of elasticity in the unit square, for Dirichlet and Dirichlet-Neumann boundary conditions, using second order finite difference schemes. The resulting linear systems are solved by the preconditioned conjugate gradient (PCG) method with preconditioners corresponding to to the Laplace operator. The multiplication of a vector by the matrices of the resulting systems and the solution of systems with the preconditioners are performed at optimal and nearly optimal costs, respectively. For the case of Dirichlet boundary conditions, we prove the second order accuracy of the scheme in the discrete norm, symmetry of the resulting matrix and its spectral equivalence to the preconditioner. For the case of Dirichlet-Neumann boundary conditions, we prove symmetry of the resulting matrix. Numerical tests demonstrating the convergence properties of the schemes and PCG are presented.

关键词： Cauchy-Navier equations Finite difference scheme matrix decomposition algorithm Preconditioned conjugate gradient method Fast Fourier transforms

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A fast direct solver for a fourth order finite difference scheme for Poisson's equation on the unit disc in polar coordinates

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NUMERICAL algorithmS 2015年第4期70卷 727-751页

作者： Bialecki, Bernard Wright, Lyndsey Colorado Sch Mines Dept Appl Math & Stat Golden CO 80401 USA Instar Engn 6901 S Pierce St Suite 200 Littleton CO 80128 USA

We present a fourth order finite difference scheme for solving Poisson's equation on the unit disc in polar coordinates. We use a half-point shift in the r direction to avoid approximating the solution at r = 0. We derive our scheme from analysis of the local truncation error of the standard second order finite difference scheme. The resulting linear system is solved very efficiently (with cost almost proportional to the number of unknowns) using a matrix decomposition algorithm with fast Fourier transforms.

关键词： Poisson's equation Polar coordinates Finite difference scheme Local truncation error matrix decomposition algorithm Fast Fourier transforms

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Energy Efficient Data Flow Transformation for Givens Rotation based QR decomposition

Energy Efficient Data Flow Transformation for Givens Rotatio...

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Design, Automation and Test in Europe Conference and Exhibition (DATE)

作者： Sharma, Namita Panda, Preeti Ranjan Li, Min Agrawal, Prashant Catthoor, Francky Indian Inst Technol Delhi New Delhi India IMEC Leuven Belgium

ISBN: (纸本)9783981537024

QR decomposition (QRD) is a typical matrix decomposition algorithm that shares many common features with other algorithms such as LU and Cholesky decomposition. The principle can be realized in a large number of valid processing sequences that differ significantly in the number of memory accesses and computations, and hence, the overall implementation energy. With modern low power embedded processors evolving towards register files with wide memory interfaces and vector functional units (FUs), the data flow in matrix decomposition algorithms needs to be carefully devised to achieve energy efficient implementation. In this paper, we present an efficient data flow transformation strategy for the Givens Rotation based QRD that optimizes data memory accesses. We also explore different possible implementations for QRD of multiple matrices using the SIMD feature of the processor. With the proposed data flow transformation, a reduction of up to 36% is achieved in the overall energy over conventional QRD sequences.

关键词： MIMO communication data flow computing energy conservation matrix decomposition optimisation Givens Rotation QR decomposition SIMD data memory access energy efficient data flow transformation matrix decomposition algorithm Computer architecture matrix converters matrix decomposition Program processors Registers Sequential analysis Vectors

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A Fast Numerical algorithm for Calculating Electromagnetic Scattering from an Object above a Rough Surface

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ELECTROMAGNETICS 2013年第1期33卷 10-22页

作者： An, Yuyuan Wang, Daoxiang Chen, Ru-Shan Nanjing Univ Sci & Technol Dept Commun Engn Nanjing 210094 Jiangsu Peoples R China

A fast numerical algorithm is proposed for calculating the difference field radar cross-section of an object above a rough surface. The electric-field integral equation of the difference of the induced current on the rough surface and the induced current on the object is derived, which is solved by an iterative solver. The characteristic basis functions are used to calculate the induced current on the rough surface, which is part of the right-hand side of the system. It is observed that the coupling matrices (nonself-block interactions of the rough surface and the interactions between the object and the rough surface) are rank deficient. The matrix decomposition algorithm is used and extended to compress the coupling matrices. Numerical examples show that the characteristic basis functions method combined with the matrix decomposition algorithm can greatly reduce the CPU time and memory cost. The accuracy and efficiency are discussed by numerical examples.

关键词： characteristic basis functions difference scattering matrix decomposition algorithm rough surface

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