On the tripling algorithm for large-scale nonlinear matrix equations with low rank structure

Dong, Ning; Yu, Bo

doi:10.1016/j.cam.2015.03.036

Cited by 3 publications

(2 citation statements)

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“…T (k) m be factor matrices generated by the FADI iteration for solving (6). For each i = 1, 2, ..., J k and m = 0, 1, ...r − 1, denote by…”

Section: Structured Shamanskii Methodsmentioning

confidence: 99%

“…For example, the classic Newton's method according to the EI above, has the efficiency √ 2 = 1.4142, since it converges quadratically with the requirement of two pieces of information (one function evaluation and one derivative evaluation). Regarding iterations in the form of vector or matrix, an evaluation index in terms of flop counts is more appropriate [6,9]. For structured Newton's method, the computation cost for each iteration x (k) is about (21J k − 10)n, where J k is the number of FADI iterations in each Newton step.…”

Section: Introductionmentioning

confidence: 99%

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Structured Shamanskii methods for Chandrasekhar equation arising from radiation

Dong¹,

Bai²,

Meng³

2020

Proc. Estonian Acad. Sci.

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The Chandrasekhar equation describes the particles emerging from the atmospheric radiation and its solution of physical significance is the minimal positive solution. This paper analyses the efficiency index of Newton's iteration in detail, which then helps to design a structured Shamanskii method for calculating the minimal positive solution. The monotone convergence of the presented algorithm is subsequently established as well as the elementary monotonicity of the solution. Preliminary numerical experiments are listed to indicate that the newely developed two-step Shamanskii method outperforms the Newton's method in terms of CPU time and iterative number with almost no loss in accuracy.

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“…T (k) m be factor matrices generated by the FADI iteration for solving (6). For each i = 1, 2, ..., J k and m = 0, 1, ...r − 1, denote by…”

Section: Structured Shamanskii Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%