Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of...Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.展开更多
Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which...Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which increases the programming complexity of and limits the parallelizability of the whole simulation.In this paper,a new adaptive preconditioned Jacobian-free Newton-GMRES(m)method is proposed to be applied to dynamic simulations of power systems.This new method has totally Jacobian-free characteristics,which saves calculations and storages of Jacobian matrixes and features strong parallelizability.Moreover,several speedup strategies are introduced to enhance efficiency and parallelizability of overall computations.Numerical tests are carried out on IEEE standard test systems and results show that in series computing environment,simulations based on the proposed method have comparable speed to those based on classical Newton-Raphson methods.展开更多
基金Supported by the National Natural Science Foundation of China(12001395)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002018)+1 种基金Research Project Supported by Shanxi Scholarship Council of China(2022-169)Graduate Education Innovation Project of Taiyuan Normal University(SYYJSYC-2314)。
文摘Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51277104 and 51207076)the National High-Tech Research & Development Program of China ("863" Program) (Grant No.2012AA050217)+1 种基金the Postdoctoral Science Foundation of China (Grant No.2012M510441)Tsinghua University Initiative Scientific Research Program (Grant No. 20121087926)
文摘Dynamic simulation is one of the most complex and important computations for power systems researches.Traditional solutions based on normal Newton iterations almost all depend on evaluations of Jacobian matrixes,which increases the programming complexity of and limits the parallelizability of the whole simulation.In this paper,a new adaptive preconditioned Jacobian-free Newton-GMRES(m)method is proposed to be applied to dynamic simulations of power systems.This new method has totally Jacobian-free characteristics,which saves calculations and storages of Jacobian matrixes and features strong parallelizability.Moreover,several speedup strategies are introduced to enhance efficiency and parallelizability of overall computations.Numerical tests are carried out on IEEE standard test systems and results show that in series computing environment,simulations based on the proposed method have comparable speed to those based on classical Newton-Raphson methods.
