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Approximate Schur-Block ILU Preconditioners for Regularized Solution of Discrete Ill-Posed Problems
المؤلفون المشاركون
Iyikal, Ovgu C.
Cival Buranay, S.
المصدر
Mathematical Problems in Engineering
العدد
المجلد 2019، العدد 2019 (31 ديسمبر/كانون الأول 2019)، ص ص. 1-18، 18ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2019-04-24
دولة النشر
مصر
عدد الصفحات
18
التخصصات الرئيسية
الملخص EN
High order iterative methods with a recurrence formula for approximate matrix inversion are proposed such that the matrix multiplications and additions in the calculation of matrix polynomials for the hyperpower methods of orders of convergence p = 4 k + 3 , where k ≥ 1 is integer, are reduced through factorizations and nested loops in which the iterations are defined using a recurrence formula.
Therefore, the computational cost is lowered from κ = 4 k + 3 to κ = k + 4 matrix multiplications per step.
An algorithm is proposed to obtain regularized solution of ill-posed discrete problems with noisy data by constructing approximate Schur-Block Incomplete LU (Schur-BILU) preconditioner and by preconditioning the one step stationary iterative method.
From the proposed methods of approximate matrix inversion, the methods of orders p = 7,11,15,19 are applied for approximating the Schur complement matrices.
This algorithm is applied to solve two problems of Fredholm integral equation of first kind.
The first example is the harmonic continuation problem and the second example is Phillip’s problem.
Furthermore, experimental study on some nonsymmetric linear systems of coefficient matrices with strong indefinite symmetric components from Harwell-Boeing collection is also given.
Numerical analysis for the regularized solutions of the considered problems is given and numerical comparisons with methods from the literature are provided through tables and figures.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Cival Buranay, S.& Iyikal, Ovgu C.. 2019. Approximate Schur-Block ILU Preconditioners for Regularized Solution of Discrete Ill-Posed Problems. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-18.
https://search.emarefa.net/detail/BIM-1194557
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Cival Buranay, S.& Iyikal, Ovgu C.. Approximate Schur-Block ILU Preconditioners for Regularized Solution of Discrete Ill-Posed Problems. Mathematical Problems in Engineering No. 2019 (2019), pp.1-18.
https://search.emarefa.net/detail/BIM-1194557
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Cival Buranay, S.& Iyikal, Ovgu C.. Approximate Schur-Block ILU Preconditioners for Regularized Solution of Discrete Ill-Posed Problems. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-18.
https://search.emarefa.net/detail/BIM-1194557
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1194557
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