Geodesic
Regularized iterative method for III-posed linear systems based on matrix splitting
Filomat, Tome 35 (2021) no. 4, p. 1343

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DOI

In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov's regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The convergence of such a well-posed system is discussed by using different types of matrix splittings. Comparison analysis of both systems are studied by operating certain types of weak splittings. Further, we have extended the double splitting of [Song J. and Song Y, Calcolo 48(3), 245–260, 2011] to double weak splitting of type II for nonsingular symmetric matrices. In addition to that, some more comparison results are presented with the help of such weak double splittings of type I and type II
DOI : 10.2298/FIL2104343N
Classification : 15A09, 65F10, 65F22
Keywords: Moore-Penrose inverse, Proper splitting, Weak splitting, Double weak splitting, Iterative regularization methods 
Ashish Kumar Nandi; Jajati Keshari Sahoo. Regularized iterative method for III-posed linear systems based on matrix splitting. Filomat, Tome 35 (2021) no. 4, p. 1343 . doi: 10.2298/FIL2104343N
@article{10_2298_FIL2104343N,
     author = {Ashish Kumar Nandi and Jajati Keshari Sahoo},
     title = {Regularized iterative method for {III-posed} linear systems based on matrix splitting},
     journal = {Filomat},
     pages = {1343 },
     year = {2021},
     volume = {35},
     number = {4},
     doi = {10.2298/FIL2104343N},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2104343N/}
}
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