scholarly journals On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems

2018 ◽  
Vol 36 (3) ◽  
pp. 155-172
Author(s):  
Lakhdar Elbouyahyaoui ◽  
Mohammed Heyouni
Keyword(s):  
Linear Systems ◽  
Sparse Matrix ◽  
Coefficient Matrix ◽  
University Of Florida ◽  
Block Arnoldi ◽  
The Matrix ◽  
Multiple Linear Systems ◽  
The University ◽  
Theoretical Results ◽  
Methods Numerical

In the present paper, we are concerned by weighted Arnoldi like methods for solving large and sparse linear systems that have different right-hand sides but have the same coefficient matrix. We first give detailed descriptions of the weighted Gram-Schmidt process and of a Ruhe variant of the weighted block Arnoldi algorithm. We also establish some theoretical results that links the iterates of the weighted block Arnoldi process to those of the non weighted one. Then, to accelerate the convergence of the classical restarted block and seed GMRES methods, we introduce the weighted restarted block and seed GMRES methods. Numerical experiments that are done with different matrices coming from the Matrix Market repository or from the university of Florida sparse matrix collection are reported at the end of this work in order to compare the performance and show the effectiveness of the proposed methods.

A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems

2017 ◽  
Vol 7 (4) ◽  
pp. 827-836
Author(s):  
Ze-Jia Xie ◽  
Xiao-Qing Jin ◽  
Zhi Zhao
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
Indefinite Systems ◽  
Indefinite Linear Systems ◽  
Theoretical Results

AbstractSome convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.

scholarly journals A Modified SSOR Preconditioning Strategy for Helmholtz Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Shi-Liang Wu ◽  
Cui-Xia Li
Keyword(s):  
Convergence Rate ◽  
Linear Systems ◽  
Iterative Methods ◽  
Low Cost ◽  
Computational Cost ◽  
Coefficient Matrix ◽  
Computational Time ◽  
Helmholtz Equations ◽  
Speed Up ◽  
Methods Numerical

The finite difference method discretization of Helmholtz equations usually leads to the large spare linear systems. Since the coefficient matrix is frequently indefinite, it is difficult to solve iteratively. In this paper, a modified symmetric successive overrelaxation (MSSOR) preconditioning strategy is constructed based on the coefficient matrix and employed to speed up the convergence rate of iterative methods. The idea is to increase the values of diagonal elements of the coefficient matrix to obtain better preconditioners for the original linear systems. Compared with SSOR preconditioner, MSSOR preconditioner has no additional computational cost to improve the convergence rate of iterative methods. Numerical results demonstrate that this method can reduce both the number of iterations and the computational time significantly with low cost for construction and implementation of preconditioners.

New SOR-like methods for solving the Sylvester equation

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Jakub Kierzkowski
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Relaxation Method ◽  
Sylvester Equation ◽  
Numerical Experimentation ◽  
Successive Over Relaxation ◽  
Theoretical Results ◽  
Methods Numerical

AbstractWe present new iterative methods for solving the Sylvester equation belonging to the class of SOR-like methods, based on the SOR (Successive Over-Relaxation) method for solving linear systems. We discuss convergence characteristics of the methods. Numerical experimentation results are included, illustrating the theoretical results and some other noteworthy properties of the Methods.

scholarly journals MPI+OpenMP implementation of the BiCGStab method with explicit preconditioning for the numerical solution of sparse linear systems

2019 ◽  
pp. 516-527
Author(s):  
И.Е. Капорин ◽  
О.Ю. Милюкова
Keyword(s):  
Parallel Implementation ◽  
Sparse Matrix ◽  
Triangular Matrix ◽  
Positive Definite Matrix ◽  
Test Problems ◽  
Approximate Inverse ◽  
University Of Florida ◽  
Upper Triangular Matrix ◽  
Class Of Matrices ◽  
The University

Для предобусловливания несимметричной положительно определенной разреженной матрицы рассматривается ее приближенная обратная, представленная в виде произведения нижнетреугольной и верхнетреугольной матриц. Предлагается новый способ предобусловливания положительно определенной разреженной матрицы--- метод блочного Якоби неполного обратного LU-разложения. Описан алгоритм параллельной реализации метода BiCGStab с предложенным предобусловливанием с применением MPIOpenMP-технологии. Проводится сравнение времени решения тестовых задач из коллекции разреженных матриц SuiteSparse (ранее известной как коллекция университета Флориды) методом BiCGStab с предложенным предобусловливанием и с предобусловливанием Якоби, а также с предобусловливанием блочного Якоби в сочетании с неполным треугольным разложением без заполнения. При этом используются разработанные параллельные реализации на основе MPI- или MPIOpenMP-подходов. A preconditioner for a large sparse nonsymmetric positive definite matrix is considered on the basis of its approximate inverse in the form of product of a lower triangular sparse matrix by an upper triangular matrix. For the class of matrices being considered, a new preconditioning based on the approximate block Jacobi with incomplete inverse LU-factorization preconditioning is proposed. For a parallel implementation of the corresponding preconditioned BiCGStab algorithm, the MPIOpenMP techniques are used. The timing results obtained for the MPIOpenMP and MPI implementations of the proposed preconditioning and for the Jacobi preconditioning used with the BiCGStab are compared using several test problems from the SuiteSparse collection (formerly known as the University of Florida sparse matrix collection).

scholarly journals Global Astrometric Solutions with Sparse Matrix Techniques

2000 ◽  
Vol 180 ◽  
pp. 127-131
Author(s):  
Richard L. Branham
Keyword(s):  
Linear Systems ◽  
Sparse Matrix ◽  
Nested Dissection ◽  
Numerical Experimentation ◽  
The Matrix ◽  
Hall Property ◽  
Sparse Matrix Techniques ◽  
Dynamic Data Structure ◽  
Large Linear Systems ◽  
Dynamic Hashing

AbstractModern astrometric techniques lead to large, linear systems solved by the precepts of least-squares. These systems are usually sparse, and one should take advantage of the sparsity to facilitate their solution. As long as the matrix A of the equations of condition possesses the weak Hall property, characteristic of linear systems derived from astrometric reductions, it is possible to find a sparse Cholesky factor. Before the equations of condition are accumulated, by use of the fast Givens transformation, a symbolic factorization of A using Tewarson’s length of intersection technique determines the ordering of the columns of A that result in low fill-in. The non-null elements are stored in a sparse, dynamic data structure by use of dynamic hashing. Numerical experimentation shows that this competes well with alternatives such as nested dissection, and large, but sparse, linear systems with several thousand unknowns can be solved in a reasonable amount of time, even on personal computers.

FloRunTM ‘331’ Peanut Variety

EDIS ◽  
2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Barry L. Tillman
Keyword(s):  
Seed Size ◽  
Growth Habit ◽  
Yield Potential ◽  
High Yield ◽  
University Of Florida ◽  
High Oleic ◽  
Central Stem ◽  
Research And Education ◽  
The University ◽  
High Yield Potential

FloRunTM ‘331’ peanut variety was developed by the University of Florida, Institute of Food and Agricultural Sciences, North Florida Research and Education Center near Marianna, Florida.  It was released in 2016 because it combines high yield potential with excellent disease tolerance. FloRunTM ‘331’ has a typical runner growth habit with a semi-prominent central stem and medium green foliage.  It has medium runner seed size with high oleic oil chemistry.

2011 BEEF FORAGE SURVEY RESULTS

EDIS ◽  
2016 ◽  
Vol 2016 (7) ◽  
Author(s):  
Sonja C. Crawford ◽  
Christa L. Kirby ◽  
Tycee Prevatt ◽  
Brent A. Sellers ◽  
Maria L. Silveira ◽  
...  
Keyword(s):  
Program Evaluation ◽  
Organizational Development ◽  
Management Practices ◽  
South Florida ◽  
University Of Florida ◽  
Development Unit ◽  
Survey Results ◽  
County Extension ◽  
Ranch Management ◽  
The University

The University of Florida / IFAS South Florida Beef Forage Program (SFBFP) is composed of county Extension faculty and state specialists.  The members, in conjunction with the UF/IFAS Program Evaluation and Organizational Development unit, created a survey in 1982, which is used to evaluate ranch management practices.  The survey is updated and distributed every 5 years to ranchers in 14 South Florida counties: Charlotte, Collier, DeSoto, Glades, Hardee, Hendry, Highlands, Hillsborough, Lee, Manatee, Martin, Okeechobee, Polk, and Sarasota.  The responses are anonymous.  

Socioeconomic patient benefits of a pediatric neurosurgery telemedicine clinic

2020 ◽  
Vol 25 (2) ◽  
pp. 204-208 ◽  
Author(s):  
Kelsey Hayward ◽  
Sabrina H. Han ◽  
Alexander Simko ◽  
Hector E. James ◽  
Philipp R. Aldana
Keyword(s):  
Travel Time ◽  
Cost Savings ◽  
Transportation Cost ◽  
Pediatric Neurosurgery ◽  
University Of Florida ◽  
Remote Location ◽  
Socioeconomic Data ◽  
The University ◽  
Time Away

OBJECTIVEThe objective of this study was to examine the socioeconomic benefits to the patients and families attending a regional pediatric neurosurgery telemedicine clinic (PNTMC).METHODSA PNTMC was organized by the Division of Pediatric Neurosurgery of the University of Florida College of Medicine–Jacksonville based at Wolfson Children’s Hospital and by the Children’s Medical Services (CMS) to service the Southeast Georgia Health District. Monthly clinics are held with the CMS nursing personnel at the remote location. A retrospective review of the clinic population was performed, socioeconomic data were extracted, and cost savings were calculated.RESULTSClinic visits from August 2011 through January 2017 were reviewed. Fifty-five patients were seen in a total of 268 initial and follow-up PNTMC appointments. The average round-trip distance for a family from home to the University of Florida Pediatric Neurosurgery (Jacksonville) clinic location versus the PNTMC remote location was 190 versus 56 miles, respectively. The families saved an average of 2.5 hours of travel time and 134 miles of travel distance per visit. The average transportation cost savings for all visits per family and for all families was $180 and $9711, respectively. The average lost work cost savings for all visits per family and for all families was $43 and $2337, respectively. The combined transportation and work cost savings for all visits totaled $223 per family and $12,048 for all families. Average savings of $0.68/mile and $48.50/visit in utilizing the PNTMC were calculated.CONCLUSIONSManaging pediatric neurosurgery patients and their families via telemedicine is feasible and saves families substantial travel time, travel cost, and time away from work.

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