A note on double weak splittings of type II

Shekhar, Vaibhav; Giri, Chinmay Kumar; Mishra, Debasisha

doi:10.1080/03081087.2020.1795057

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…al. [ 23 ] introduced convergence theory of type II double splittings. Motivated by the same work, we plan to study the problem of the convergence of the two-stage iteration scheme for type II splittings near future.…”

Section: Monotone Iterationsmentioning

confidence: 99%

On convergence of two-stage iterative scheme

Shekhar

Giri²,

Mishra

2021

J Anal

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Climent and Perea [Journal of Computational and Applied Mathematics 58:43–48, 2003; MR2013603] proposed first the convergence theory of two-stage iterative scheme for solving real rectangular linear systems. In this article, we revisit the same theory. The first main result provides some sufficient conditions which guarantee that the induced splitting from a two-stage iterative scheme is a proper weak regular splitting. We then establish a few comparison results. Out of these, many are even new in nonsingular matrix setting. Further, we study the monotone convergence theory of the two-stage iterative method. Besides these, we also prove the uniqueness of a proper splitting of a rectangular matrix under certain assumptions.

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Section: Monotone Iterationsmentioning

confidence: 99%

On convergence of two-stage iterative scheme

Shekhar

Giri²,

Mishra

2021

J Anal

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Alternating stationary iterative methods based on double splittings

Nandi

Shekhar

Mishra

et al. 2021

Computers & Mathematics with Applications

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More on proper nonnegative splittings of rectangular matrices

Huang¹,

Miao

2020

MATH

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<abstract><p>In this paper, we introduce a mixed numerical technique for solving fractional differential equations (FDEs) by combining Chebyshev collocation methods and a piecewise quadratic quadrature rule. For getting solutions at each integration step, the fractional integration is calculated in two intervals-all previous time intervals and the current time integration step. The solution at the current integration step is calculated by using Chebyshev interpolating polynomials. To remove a singularity which belongs originally to the FDEs, Lagrangian interpolating technique is considered since the Chebyshev interpolating polynomial can be rewritten as a Lagrangian interpolating form. Moreover, for calculating the fractional integral on the whole previous time intervals, a piecewise quadratic quadrature technique is applied to get higher accuracy. Several numerical experiments demonstrate the efficiency of the proposed method and show numerically convergence orders for both linear and nonlinear cases.</p></abstract>

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A note on double weak splittings of type II

Cited by 4 publications

References 17 publications

On convergence of two-stage iterative scheme

On convergence of two-stage iterative scheme

Alternating stationary iterative methods based on double splittings

More on proper nonnegative splittings of rectangular matrices

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