A new iteration method for a class of complex symmetric linear systems

Wang, Teng; Zheng, Qingqing; Lu, Linzhang

doi:10.1016/j.cam.2017.05.002

Cited by 44 publications

(23 citation statements)

References 25 publications

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“…In our numerical experiments, we compare the proposed DSM with 1. the two parameter two-step scale-splitting (TTSCSP) method defined in the introduction, as well as 2. the preconditioned Hermitian/skew-Hermitian splitting (PMHSS) method [5], and 3. the combination method of real and imaginary parts (CRI) [19]. The formal definitions of the latter two methods are given below.…”

Section: Existing Methods Used For Comparisonmentioning

confidence: 99%

“…The CRI iteration method [19]: Given u (0) ∈ C n , generate a sequence {u (k) } such that (αT + W )u (k+ 1 2 ) = (α − i)T u (k) + b, (αW + T )u (k+1) = (α + i)W u (k+ 1 2 ) − ib, where α is a given positive real number.…”

Section: Existing Methods Used For Comparisonmentioning

confidence: 99%

“…In recent years, many efficient iterative methods have been proposed for the numerical solutions of complex symmetric linear systems. Among these, some notable ones are the Hermitian/skew-Hermitian splitting (HSS) method [6] due to Bai et al, its modified version (MHSS) [3], preconditioned version (PMHSS) [5], the combination method of real and imaginary parts (CRI) [19] due to Wang et al…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new double-step method for solving complex Helmholtz equation

Salkuyeh

Siahkoalaei

2020

Hacettepe Journal of Mathematics and Statistics

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We present a new double-step iteration method for solving the systems of linear equations that arise from finite difference discretizations of the complex Helmholtz equations. Convergence analysis of the method is discussed. An upper bound on the spectral radius of the iteration matrix of the method is presented and the parameter which minimizes this upper bound is computed. The proposed method is compared theoretically and numerically with some existing methods.

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Section: Existing Methods Used For Comparisonmentioning

confidence: 99%

Section: Existing Methods Used For Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new double-step method for solving complex Helmholtz equation

Salkuyeh

Siahkoalaei

2020

Hacettepe Journal of Mathematics and Statistics

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“…The sparse observation matrix plays an important role in the reconstruction algorithm. In [5], Wang et al expounded the advantages of the compressed sensing theory in solving the problem of information redundancy for the traditional signal acquisition process. They analyzed the construction of the compressed sensing measurement matrix from four aspects.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Bat Algorithm Optimization Strategy for Observation Matrix

et al. 2019

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Bat algorithm, as an optimization strategy of the observation matrix, has been widely used. Observation matrix has a direct impact on the reconstructed signal accuracy as a projection transformation matrix, and it has been widely used in various algorithms. However, for the traditional experimental process, randomly generated observation matrices often result in a larger reconstruction error and unstable reconstruction results. Therefore, it is a challenge to retain more feature information of the original signal and reduce reconstruction error. To obtain a more accurate reconstruction signal and less memory space, it is important to select an effective compression and reconstruction strategy. To solve this problem, an adaptive bat algorithm is proposed to optimize the observation matrix in this paper. For the adaptive bat algorithm, we design a dynamic adjustment strategy of the optimal radius to improve its global convergence ability. The results of our simulation experiments verify that, compared with other algorithms, it can effectively reduce the reconstruction error and has stronger robustness.

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“…In 2016, a scale-splitting (SCSP) iteration method [15] was constructed by multiplying a complex number (α−i) through both sides of (1.2), numerical results show that it is efficient to address (1.2). Subsequently, some generalized versions of this SCSP iteration method were developed, such as double-step scale splitting (DSS) iteration method [16], generalized DSS-SOR iteration method [17] and combining real and imaginary part iteration method [18]. They are also considerable to deal with linear system (1.2).…”

Section: Introductionmentioning

confidence: 99%

On symmetric block triangular splitting iteration method for a class of complex symmetric system of linear equations

Zhang

2018

Applied Mathematics Letters

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A new iteration method for a class of complex symmetric linear systems

Cited by 44 publications

References 25 publications

A new double-step method for solving complex Helmholtz equation

A new double-step method for solving complex Helmholtz equation

Adaptive Bat Algorithm Optimization Strategy for Observation Matrix

On symmetric block triangular splitting iteration method for a class of complex symmetric system of linear equations

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