Browsing by Author "Krishnendu, R."

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    Finite dimensional realization of the FTR method with Raus and Gfrerer type discrepancy principle
    (Springer-Verlag Italia s.r.l., 2023) George, S.; Padikkal, J.; Krishnendu, R.
    It is known that the standard Tikhonov regularization methods oversmoothen the solution x^ of the ill-posed equation T(x) = y, so the computed approximate solution lacks many inherent details that are expected in the desired solution. To rectify this problem, Fractional Tikhonov Regularization (FTR) method have been introduced. Kanagaraj et al. (J Appl Math Comput 63(1):87–105, 2020), studied FTR method for solving ill-posed problems. Techniques are developed to study the Finite Dimensional FTR (FDFTR) method. We also study Raus and Gfrerer type discrepancy principle for FDFTR method and compare the numerical results with other discrepancy principles of the same type. © 2023, The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature.
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    On Newton’s Midpoint-Type Iterative Scheme’s Convergence
    (Springer, 2022) Krishnendu, R.; Saeed, M.; George, S.; Padikkal, J.
    This paper introduce new three step iterative schemes with order of convergence five and six for solving nonlinear equations in Banach spaces. The proposed scheme’s convergence is assessed using assumptions on the operator’s derivatives up to order two. Unlike earlier studies, the convergence study of these methods are not based on the Taylor’s expansion. Numerical examples and Basin of attractions are given in this study © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    On the convergence of Homeier method and its extensions
    (Springer Science and Business Media B.V., 2022) Muhammed Saeed, K.; Krishnendu, R.; George, S.; Padikkal, J.
    A third-order Homeier method for solving equations in Banach space is studied. Using assumptions on the first and second derivatives, we obtained third-order convergence. Our technique does not involve Taylor series expansion and can be extended to similar higher-order methods. We have given two extensions of the method with orders five and six. Examples with radii of convergence and basins of attraction are provided. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.