Advances in Operator Theory

Comparison results for proper multisplittings of rectangular matrices

Chinmay Kumar Giri and Debasisha Mishra

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Abstract

The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is practically very slow in many cases. Thus, works on improving the speed of the iteration scheme have attracted great interest. In this direction, comparison of the rate of convergence of the iteration schemes produced by two matrix splittings is very useful. But, in the case of matrices having many matrix splittings, this process is time-consuming. The main goal of the current article is to provide a solution to the above issue by using proper multisplittings. To this end, we propose a few comparison theorems for proper weak regular splittings and proper nonnegative splittings first. We then derive convergence and comparison theorems for proper multisplittings with the help of the theory of proper weak regular splittings.

Article information

Source
Adv. Oper. Theory, Volume 2, Number 3 (2017), 334-352.

Dates
Received: 5 January 2017
Accepted: 19 May 2017
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431680

Digital Object Identifier
doi:10.22034/aot.1701-1088

Mathematical Reviews number (MathSciNet)
MR3730058

Zentralblatt MATH identifier
1372.65115

Subjects
Primary: 15A09: Matrix inversion, generalized inverses
Secondary: 65F15: Eigenvalues, eigenvectors 65F20: Overdetermined systems, pseudoinverses

Keywords
Moore–Penrose inverse proper splitting multisplittings convergence theorem comparison theorem

Citation

Giri, Chinmay Kumar; Mishra, Debasisha. Comparison results for proper multisplittings of rectangular matrices. Adv. Oper. Theory 2 (2017), no. 3, 334--352. doi:10.22034/aot.1701-1088. https://projecteuclid.org/euclid.aot/1512431680


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