In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent im...In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.展开更多
We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterativ...We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterative method is adopted as a smoother,which can accelerate the convergence of the new methods.We also give the convergence analysis of these methods.Finally,some numerical experiments confirm the theoretical analysis and show that the new methods can achieve high efficiency and lower costs simultaneously.展开更多
设E是一实的p-一致光滑的B anach空间(1<p≤2),D是E的非空闭凸子集而且是E的非扩张收缩核.设T∶D→E是具有序列{kn}[1,∞),limn→∞kn=1的非自渐近非扩张映象,P∶E→D是一非扩张保核收缩.本文证明了在一定条件下,由修正的R e ich-Tak...设E是一实的p-一致光滑的B anach空间(1<p≤2),D是E的非空闭凸子集而且是E的非扩张收缩核.设T∶D→E是具有序列{kn}[1,∞),limn→∞kn=1的非自渐近非扩张映象,P∶E→D是一非扩张保核收缩.本文证明了在一定条件下,由修正的R e ich-Takahash i迭代法(1)和(2)式定义的迭代序列{xn}强收敛于非自渐近非扩张映象T的不动点.展开更多
文摘In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.
基金National Natural Science Foundation of China(12161027)Guangxi Natural Science Foundation,China(2020GXNSFAA159143)Science and Technology Project of Guangxi,China(AD23023002).
文摘We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterative method is adopted as a smoother,which can accelerate the convergence of the new methods.We also give the convergence analysis of these methods.Finally,some numerical experiments confirm the theoretical analysis and show that the new methods can achieve high efficiency and lower costs simultaneously.
文摘设E是一实的p-一致光滑的B anach空间(1<p≤2),D是E的非空闭凸子集而且是E的非扩张收缩核.设T∶D→E是具有序列{kn}[1,∞),limn→∞kn=1的非自渐近非扩张映象,P∶E→D是一非扩张保核收缩.本文证明了在一定条件下,由修正的R e ich-Takahash i迭代法(1)和(2)式定义的迭代序列{xn}强收敛于非自渐近非扩张映象T的不动点.
