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An even faster solver for general systems of equations [chapter]

Christian Fecht, Helmut Seidl
1996 Lecture Notes in Computer Science  
We present a new algorithm which computes a partial approximate solution for a system of equations.  ...  , and it is general in that the algorithm does not depend on any speci c properties of right-hand sides of equations.  ...  We are indepted for valuable discussions on xpoint iteration strategies to Andreas Neumann and the German Scholar Olympic Team for Computer Science.  ... 
doi:10.1007/3-540-61739-6_42 fatcat:prjdiofkf5ehdpuaagkdkiwcha

Analog and Hybrid Computation Approaches for Static Power Flow

Aaron Leger, Chika Nwankpa
2007 2007 40th Annual Hawaii International Conference on System Sciences (HICSS'07)  
This paper presents a static mathematical model of an AC power system and methods of implementation for both an analog and a hybrid computation scheme.  ...  PSpice simulation results verify the power system models and insight is provided on implementation for large scale systems.  ...  An analog static power flow solver could provide solutions even faster than prior dynamic approaches.  ... 
doi:10.1109/hicss.2007.73 dblp:conf/hicss/LegerN07 fatcat:m6q6exwxevcrbhpvlvlcb55dpe

A unified boundary element method for the analysis of sound and shell-like structure interactions. II. Efficient solution techniques

Shaohai Chen, Yijun Liu, Xinyu Dou
2000 Journal of the Acoustical Society of America  
An iterative solver, namely, the quasiminimal residual method ͑QMR͒, is selected among others and found to be very favorable over the direct solver for solving the linear systems of equations with complex  ...  Efficient solution methods are investigated in this paper for solving the linear system of equations resulting from the recently developed boundary element method ͑BEM͒ for the coupled structural acoustic  ...  The solution time in the case of 4902 equations was more than five times faster than that of a direct solver, even with a stringent stopping criterion (10 Ϫ7 ).  ... 
doi:10.1121/1.1323719 fatcat:mk45dqeihfhyded5jalwxcnzbe

Approximated Relative Pose Solvers for Efficient Camera Motion Estimation [chapter]

Jonathan Ventura, Clemens Arth, Vincent Lepetit
2015 Lecture Notes in Computer Science  
The reasons for this speed-up are twofold. First, by approximating the rotation matrix to first order, we obtain a smaller polynomial system to be solved.  ...  Second, because of the small rotation assumption, we can use linearization and truncation of higher-order terms to quickly obtain a single solution.  ...  However, in this work we choose to solve for the rotation because it leads to an even faster solver based on linearization and truncation of higher-order terms.  ... 
doi:10.1007/978-3-319-16178-5_12 fatcat:7xo24odognborfi2rqzfyzusn4

A Class of New Preconditioners for Linear Solvers Used in Power System Time-Domain Simulation

Siddhartha Kumar Khaitan, James D. McCalley
2010 IEEE Transactions on Power Systems  
The system of linear equations results from an attempt to solve the differential algebraic equations (DAE) encountered in the power system dynamic simulation.  ...  In this paper, a new class of preconditioners for iterative methods is proposed for the solution of linear equations that arise in the time-domain simulation of the power system.  ...  There are more than 500 contingencies for this system. An analysis of just 500 contingencies would save more than 800 days, which is huge even for this system.  ... 
doi:10.1109/tpwrs.2010.2045011 fatcat:dvf5ffuqmraivlg3p3mxvjsda4

On the effect of linear algebra implementations in real-time multibody system dynamics

Manuel González, Francisco González, Daniel Dopico, Alberto Luaces
2007 Computational Mechanics  
Different implementations for this method, both dense and sparse, have been developed, using a number of linear algebra software libraries (including sparse linear equation solvers) and sparse matrix computation  ...  Finally, we provide guidelines to increase the efficiency of MBS dynamic simulations, by recommending some optimization techniques and the linear equation solvers which provide the best compromise between  ...  The same argument applies to iterative solvers and out-of-core solvers designed for very big linear equation systems.  ... 
doi:10.1007/s00466-007-0218-2 fatcat:ykxclgtntfe2nlqxd7gszrmkku

Beyond Gröbner Bases: Basis Selection for Minimal Solvers [article]

Viktor Larsson, Magnus Oskarsson, Kalle Åström, Alge Wallis, Zuzana Kukelova, Tomas Pajdla
2018 arXiv   pre-print
In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases.  ...  These monomial bases have traditionally been based on a Gr\"obner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way.  ...  Acknowledgements This work is supported by the strategic research projects ELLIIT and eSSENCE, Swedish Foundation for Strategic Research project "Semantic Mapping and Visual Navigation for Smart Robots  ... 
arXiv:1803.04360v1 fatcat:asxaoaonlfcl7mysnj6bsbddgm

Beyond Grobner Bases: Basis Selection for Minimal Solvers

Viktor Larsson, Magnus Oskarsson, Kalle Astrom, Alge Wallis, Tomas Pajdla, Zuzana Kukelova
2018 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition  
In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases.  ...  These monomial bases have traditionally been based on a Gröbner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way.  ...  Building Minimal Solvers using Gröbner Fans In [29] , the state-of-the-art automatic generator for polynomial solvers has been presented and evaluated on a large test-bed of polynomial equation systems  ... 
doi:10.1109/cvpr.2018.00415 dblp:conf/cvpr/LarssonOAWKP18 fatcat:ujv5f7jncbcivcn6ri2rxgzega

Recent Progress in General Sparse Direct Solvers [chapter]

Anshul Gupta
2001 Lecture Notes in Computer Science  
During the past few years, algorithmic improvements alone have shaved almost an order of magnitude off the time required for the direct solution of general sparse systems of linear equations.  ...  In this paper, we compare the performance of some commonly used software packages for solving general sparse systems.  ...  Introduction Developing an efficient parallel, or even serial, direct solver for general sparse systems of linear equations is a challenging task that has been the subject of research for the past four  ... 
doi:10.1007/3-540-45545-0_94 fatcat:hbjlkdv2yzhgvix2xjbioezvq4

Newton-preconditioned Krylov subspace solvers for system of nonlinear equations: A numerical experiment

S. Sundar, B.K. Bhagavan, S. Prasad
2001 Applied Mathematics Letters  
In this paper, we present a numerical comparative study of the Newton-preconditioned Lanczos algorithms and Newton-preconditioned CG-like methods, with respect to convergence speed and CPU-time, by considering  ...  NEWTON METHOD FOR NONLINEAR SYSTEMS OF EQUATIONS Consider a nonlinear system of equations F(X) =0, (1) where F : R n ~ R n is a nonlinear mapping with the following properties. (1) There exists an X E  ...  The Newton method is well known for solving nonlinear system of equations.  ... 
doi:10.1016/s0893-9659(00)00135-x fatcat:fmwnh4d72bcorhhnaahjn3qrda

Real-Time Solution to the Absolute Pose Problem with Unknown Radial Distortion and Focal Length

Zuzana Kukelova, Martin Bujnak, Tomas Pajdla
2013 2013 IEEE International Conference on Computer Vision  
Our new solver is numerically more stable, more accurate, and significantly faster than the existing state-of-the-art minimal four point absolute pose solvers for this problem.  ...  Therefore it is simpler than the state-of-the-art Gröbner basis solvers. We compare our new solver with the existing state-of-theart solvers and show its usefulness on synthetic and real datasets. 1  ...  The speed-up over the general P4Pfr solver [12] is even much bigger.  ... 
doi:10.1109/iccv.2013.350 dblp:conf/iccv/KukelovaBP13 fatcat:jb5zjr2b2bcqpdneeunixbvaby

An Accelerated Iterative Linear Solver with GPUs for CFD Calculations of Unstructured Grids

Justin Williams, Christian Sarofeen, Hau Shan, Matthew Conley
2016 Procedia Computer Science  
For CFD solvers utilizing the Finite Volume Method (FVM) with implicit time stepping or a segregated pressure solver, a large portion of the computation time is spent solving a large linear system with  ...  In an effort to improve the performance of these CFD codes, in effect decreasing the time to solution of engineering problems, a conjugate gradient solver for a Finite Volume Method Solver Graphics Processing  ...  The iterative solver for the system of linear equations is a non-preconditioned Conjugate gradient method as described in [12] .  ... 
doi:10.1016/j.procs.2016.05.504 fatcat:5cs6hq2a3ngdrnuer6auly4ele

A GPU Laplacian solver for diffusion curves and Poisson image editing

Stefan Jeschke, David Cline, Peter Wonka
2009 ACM Transactions on Graphics  
Abstract We present a new Laplacian solver for minimal surfaces-surfaces having a mean curvature of zero everywhere except at some fixed (Dirichlet) boundary conditions.  ...  We also show results for real-time seamless cloning and stitching of large image panoramas.  ...  Acknowledgements We thank Orzan et al. [2008] for their drawing application and curve models as well as McCann and Pollard [2008] for making their code publicly available.  ... 
doi:10.1145/1618452.1618462 fatcat:byfexew5orgdtagv3rmvv5oe3y

Partial Symmetry in Polynomial Systems and Its Applications in Computer Vision

Yubin Kuang, Yinqiang Zheng, Kalle Astrom
2014 2014 IEEE Conference on Computer Vision and Pattern Recognition  
Algorithms for solving systems of polynomial equations are key components for solving geometry problems in computer vision.  ...  In both synthetic and real experiments, we show that utilizing partial symmetry allow us to obtain faster and more accurate polynomial solvers than the general solvers 1 .  ...  On the other hand, our solver is around three times faster than the general solver ( Table 1 ).  ... 
doi:10.1109/cvpr.2014.63 dblp:conf/cvpr/KuangZA14 fatcat:wryxtb6mzbdglnwvwru25vzcsy

GPU-based N-1 Static Security Analysis Algorithm with Preconditioned Conjugate Gradient Method

Meng Fu, Gan Zhou, Jiahao Zhao, Yanjun Feng, Huan He, Kai Liang
2020 IEEE Access  
Case studies on a practical 10828-bus system show that the GPU-based N-1 SSA algorithm with the batch-PCG solver is 4.90 times faster than a sequential algorithm on an 8-core CPU.  ...  N-1 static security analysis (SSA) is an important method for power system stability analysis that requires solving N alternating-current power flows (ACPF) for a system with N elements to obtain strictly  ...  Two kinds of solvers are generally used to solve linear equations.  ... 
doi:10.1109/access.2020.3004713 fatcat:k6wbjj6elngvfi2r376fudpibq
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