Combining Uneliminated Algebraic Formulations With Sparse Linear Solvers to Increase the Speed and Accuracy of Homotopy Path Tracking for Kinematic SynthesisSource: Journal of Computing and Information Science in Engineering:;2022:;volume( 022 ):;issue: 006::page 61007Author:Glabe, Jeffrey;Plecnik, Mark
DOI: 10.1115/1.4055241Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The method of kinematic synthesis requires finding the solution set of a system of polynomials. Parameter homotopy continuation is used to solve these systems and requires repeatedly solving systems of linear equations. For kinematic synthesis, the associated linear systems become ill-conditioned, resulting in a marked decrease in the number of solutions found due to path tracking failures. This unavoidable ill-conditioning places a premium on accurate function and matrix evaluations. Traditionally, variables are eliminated to reduce the dimension of the problem. However, this greatly increases the computational cost of evaluating the resulting functions and matrices and introduces numerical instability. We propose avoiding the elimination of variables to reduce required computations, increasing the dimension of the linear systems, but resulting in matrices that are quite sparse. We then solve these systems with sparse solvers to save memory and increase speed. We found that this combination resulted in a speedup of up to 250 × over traditional methods while maintaining the same accuracy.
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contributor author | Glabe, Jeffrey;Plecnik, Mark | |
date accessioned | 2022-12-27T23:12:45Z | |
date available | 2022-12-27T23:12:45Z | |
date copyright | 9/15/2022 12:00:00 AM | |
date issued | 2022 | |
identifier issn | 1530-9827 | |
identifier other | jcise_22_6_061007.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4288120 | |
description abstract | The method of kinematic synthesis requires finding the solution set of a system of polynomials. Parameter homotopy continuation is used to solve these systems and requires repeatedly solving systems of linear equations. For kinematic synthesis, the associated linear systems become ill-conditioned, resulting in a marked decrease in the number of solutions found due to path tracking failures. This unavoidable ill-conditioning places a premium on accurate function and matrix evaluations. Traditionally, variables are eliminated to reduce the dimension of the problem. However, this greatly increases the computational cost of evaluating the resulting functions and matrices and introduces numerical instability. We propose avoiding the elimination of variables to reduce required computations, increasing the dimension of the linear systems, but resulting in matrices that are quite sparse. We then solve these systems with sparse solvers to save memory and increase speed. We found that this combination resulted in a speedup of up to 250 × over traditional methods while maintaining the same accuracy. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Combining Uneliminated Algebraic Formulations With Sparse Linear Solvers to Increase the Speed and Accuracy of Homotopy Path Tracking for Kinematic Synthesis | |
type | Journal Paper | |
journal volume | 22 | |
journal issue | 6 | |
journal title | Journal of Computing and Information Science in Engineering | |
identifier doi | 10.1115/1.4055241 | |
journal fristpage | 61007 | |
journal lastpage | 61007_11 | |
page | 11 | |
tree | Journal of Computing and Information Science in Engineering:;2022:;volume( 022 ):;issue: 006 | |
contenttype | Fulltext |