Geodesic
Multiple iterative solution of linear algebraic systems with a~partially varying matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVI, Tome 419 (2013), pp. 16-25

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An iterative algorithm for solving a series of linear algebraic systems with a partially varying coefficient matrix is suggested. Simple formulas for evaluating the speed up obtained are derived and used in choosing the related parameters. As examples, the choice of the drop tolerance and of the initial guess are considered. Multiple solution of linear systems of orders 708, 1416, 3540, and 4425 arising in computing (by the method of moments) the electric capacity of two stripes on a dielectric layer above a perfect conductive plane in the range of dielectric permeability is analyzed. As compared with the Gauss method, a 49 times speed up in solving 1000 linear systems of order 4425 is achieved. 
@article{ZNSL_2013_419_a1,
     author = {R. R. Akhunov and S. P. Kuksenko and V. K. Salov and T. R. Gazizov},
     title = {Multiple iterative solution of linear algebraic systems with a~partially varying matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {16--25},
     publisher = {mathdoc},
     volume = {419},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_419_a1/}
}
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R. R. Akhunov; S. P. Kuksenko; V. K. Salov; T. R. Gazizov. Multiple iterative solution of linear algebraic systems with a~partially varying matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVI, Tome 419 (2013), pp. 16-25. http://geodesic.mathdoc.fr/item/ZNSL_2013_419_a1/