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A robust and efficient proposal for solving linear systems arising in interior-point methods for linear programming

María D. Gonzalez-Lima, Aurelio R. L. Oliveira, Danilo E. Oliveira
2013 Computational optimization and applications  
The computational burden of primal-dual interior point methods for linear programming relies on the computation of the search direction by solving one or more linear systems per iterations.  ...  The objective of this work is to study an efficient and robust way of solving these systems for large-scale sparse problems.  ...  We present a way of solving the stable system that it is competitive, in terms of running time, with the traditional normal equations approach for some large, sparse linear programming problems.  ... 
doi:10.1007/s10589-013-9572-5 fatcat:qwf7udvz4jbfpj4j5hxremjw5i

Page 1730 of Mathematical Reviews Vol. 48, Issue 5 [page]

1974 Mathematical Reviews  
Reid, On the method of conjugate gradients for the solution of large sparse systems of linear equations (pp. 231-254); Ralph A.  ...  Tuff, A direct method for the solution of large sparse symmetric simul- taneous equations (pp. 97-104); R. Baumann, Sparseness in power systems equations (pp. 105-125); M. E.  ... 

Parallel Solution of Large-Scale and Sparse Generalized Algebraic Riccati Equations [chapter]

José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí
2006 Lecture Notes in Computer Science  
We discuss a parallel algorithm for the solution of large-scale generalized algebraic Riccati equations with dimension up to O(10 5 ).  ...  We survey the numerical algorithms underlying the implementation of the method, in particular, a Newton-type iterative solver for the generalized Riccati equation and an LR-ADI solver for the generalized  ...  Quintana-Ortí were supported by the CICYT project TIN2005-09037-C02-02 and FEDER, and project No. P1B-2004-6 of the Fundación Caixa-Castellón/Bancaixa and UJI.  ... 
doi:10.1007/11823285_74 fatcat:r3ol5ekygvb6dky3eajpzsknnm

Page 1004 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews  
methods for sparse matrices and their use in the numerical solution of large linear least squares problems.  ...  The author proposes a universal algorithm called the directional perturbation least squares (DPLS) algorithm, which can give op- timal solutions of an overdetermined system of linear equations in L2,Lo0  ... 

Solving Large Sparse Lyapunov Equations on Parallel Computers [chapter]

José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí
2002 Lecture Notes in Computer Science  
This paper describes the parallelization of the low-rank ADI iteration for the solution of large-scale, sparse Lyapunov equations.  ...  The only relevant operations involved in the method are matrix-vector products and the solution of linear systems.  ...  The algorithm benefits from the availability and efficiency of parallel kernels for the matrixvector product and the solution of sparse linear systems using direct methods.  ... 
doi:10.1007/3-540-45706-2_95 fatcat:vyzazexoqzcqpgjggida7a2msu

Page 2102 of Mathematical Reviews Vol. , Issue 83e [page]

1983 Mathematical Reviews  
Authors’ summary: “This paper presents a version of the preconditioned conjugate gradient algorithm as applied to the solution of a large and sparse system of linear algebraic equations 83e:65065  ...  Author’s introduction: “The solution vector x to the linear system Ax = b, where x and b are n-vectors and A is a sparse n Xn matrix, is often a discrete approximation to a solution of a differential equation  ... 

A GPU-Based Transient Stability Simulation Using Runge-Kutta Integration Algorithm

Zhijun Qin, Yunhe Hou
2013 International Journal of Smart Grid and Clean Energy  
The differential equations of dynamic components are evaluated in GPU, while the linear network equations are solved in CPU using sparse direct solver.  ...  Simulation on IEEE 22-bus power system with 6 generators is reported to validate the feasibility of the proposed method.  ...  Since solving dense linear systems of equations is a fundamental problem in scientific computing, it is critical to accelerate the solution of large-scale linear equations as fast as possible.  ... 
doi:10.12720/sgce.2.1.32-39 fatcat:3mh6ko7mdrbxtf76kyv2nen3u4

Preconditioning Techniques for Sparse Linear Systems

Massimiliano Ferronato, Edmond Chow, Kok-Kwang Phoon
2012 Journal of Applied Mathematics  
Acknowlegments We would like to thank the authors for their valuable contributions and the anonymous reviewers for their thorough and insightful comments that brought this special Issue to fruition.  ...  Direct methods for sparse linear systems often represent the de facto solver in several commercial codes on the basis of their robustness and reliability.  ...  Saad, Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, 2003 than a rigorous mathematical exercise.  ... 
doi:10.1155/2012/518165 fatcat:pnprhaohazdi3kuxhjb3yurov4

Page 3161 of Mathematical Reviews Vol. , Issue 88f [page]

1988 Mathematical Reviews  
ISBN 0-19-853408-6 The authors have written an excellent book on the present state of affairs in the solution of large sparse matrix systems by direct meth- ods.  ...  This paper deals with the iterative solutions of large systems of linear equations such as those arising from finite difference ap- proximations to elliptic partial differential equations.  ... 

Page 1627 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
Iterative methods for solving large sparse linear systems. Numerical solutions of partial differential equations ( Parkville, 1981), pp. 367-396, North-Holland, Amsterdam, 1982.  ...  that of one system of large asymmetric sparse linear algebraic equations Ax = b with variable order.  ... 

Page 1205 of Mathematical Reviews Vol. 49, Issue 3 [page]

1975 Mathematical Reviews  
K. 6582 On the method of conjugate gradients for the solution of large sparse systems of linear equations. Large sparse sets of linear equations (Proc. Conf., St.  ...  W. 6583 Conjugate direction methods for solving systems of linear equations. Numer. Math. 21 (1973/74), 285-297.  ... 

Page 2880 of Mathematical Reviews Vol. 58, Issue 4 [page]

1979 Mathematical Reviews  
The authors study direct methods for solving large sparse systems of linear equations.  ...  .; Kehat, E. 58 # 19068 A direct method for the solution of large sparse systems of linear equations. Comput. J. 19 (1976), no. 4, 353-359.  ... 

Efficient Solution of Spacecraft Thermal Models Using Preconditioned Conjugate Gradient Methods

C. K. Krishnaprakas
1998 Journal of Spacecraft and Rockets  
For small or moderate linear systems, a conventional direct method is efficient for a solution.  ...  Iterative methods and conjugate gradient methods offer several advantages for the solu- tion of large, randomly packed, sparse, linear systems over direct methods.  ... 
doi:10.2514/2.3413 fatcat:6l4x47f7nzdn5dt5lkfsies7x4

Simultaneous analysis of large INTEGRAL/SPI11Based on observations with INTEGRAL, an ESA project with instruments and science data center funded by ESA member states (especially the PI countries: Denmark, France, Germany, Italy, Spain, and Switzerland), Czech Republic and Poland with participation of Russia and the USA. datasets: Optimizing the computation of the solution and its variance using sparse matrix algorithms

L. Bouchet, P. Amestoy, A. Buttari, F.-H. Rouet, M. Chauvin
2013 Astronomy and Computing  
Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods.  ...  Processing several years of data simultaneously requires computing not only the solution of a large system of equations, but also the associated uncertainties.  ...  Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods.  ... 
doi:10.1016/j.ascom.2013.03.002 fatcat:dk52pn7e45ayjhm3myz7ha3rie

Hybrid Iterative-Direct Solution Strategy For Improving The Scalability Of Nuclear Waste Management Simulations

Emmanuel Agullo
2017 Zenodo  
The enabling numerical tool is a domain decomposition solution strategy for the sparse system of linear equations resulting from the spatial discretization of the underlying PDEs (Partial Differential  ...  A concrete application is considered for assessing the benefits of using a domain decomposition sparse linear solution strategy as compared to the originally used approach, which is based on a more classical  ...  Acknowledgements This work was financially supported by the PRACE project funded in part by the EU's Horizon 2020 research and innovation programme (2014-2020) under grant agreement 653838.  ... 
doi:10.5281/zenodo.826134 fatcat:hqymvtg4kbchhme2lt5a5m6hii
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