Quotient convergence and multi-splitting methods for solving singular linear equations

Cui, Xiaoke; Wei, Yimin; Zhang, Naimin

doi:10.1007/s10092-007-0127-y

Cited by 13 publications

(5 citation statements)

References 20 publications

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“…Besides these, we would now like to recall some works in connection with the present work. Cui et al, [16] and Lin et al, [12] studied properties of convergence and quotient convergence of iterative methods for solving consistent singular linear systems with index one. Cui et al, [16] also applied the same theory to multisplittings.…”

Section: Discussionmentioning

confidence: 99%

“…Cui et al, [16] and Lin et al, [12] studied properties of convergence and quotient convergence of iterative methods for solving consistent singular linear systems with index one. Cui et al, [16] also applied the same theory to multisplittings. Note that both their works deal with matrices of index one while we do not have any restriction on index.…”

Section: Discussionmentioning

confidence: 99%

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A note on index-proper multisplittings of matrices

Baliarsingh¹,

Jena²

2015

Banach J. Math. Anal.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

A note on index-proper multisplittings of matrices

Baliarsingh¹,

Jena²

2015

Banach J. Math. Anal.

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“…By replacement of M −1 with M † , Cao [10] got the sufficient and necessary conditions for convergence of the iterative scheme. By replacement of M −1 with the Drazin inverse of M , Wei et al [26], Cui et al [13] and Lin et al [17] got some convergence results of the iterative scheme. Lee et al [16] and Cao [10] studied the convergence of the general stationary iterative method with the seminorm.…”

Section: Yanxing Cui Chuanlong Wang and Ruiping Wenmentioning

confidence: 99%

On the convergence of generalized parallel multisplitting iterative methods for semidefinite linear systems

Cui¹,

Wang²,

Wen³

2012

Numerical Algebra, Control &Amp; Optimization

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In this paper, we present the generalized stationary and nonstationary multisplitting iterative methods for positive semidefinite linear systems. We study the convergence theories of new methods and show that the quotient convergence and convergence of stationary parallel multisplitting method are equivalent under a concise condition. Finally, we prove that the generalized nonstationary parallel multisplitting method is quotient convergence with general weighting matrices.

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“…The theory of Drazin inverse has numerous applications, such as difference equations, statistics, Markov chains and numerical analysis and so on (see [2][3][4][5][6][7][8][9][10][11]). In 1977, Meyer and Rose gave the computational formula of the Drazin inverse for complex block matrix A B 0 C (A and C are square) (see [2]).…”

Section: Introductionmentioning

confidence: 99%