Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks
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DOI: 10.1007/s00211-020-01143-x
Abstract: Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods… read more here.
Keywords: block; operators two; two two; preconditioner ... See more keywords
A new version of a preconditioning method for certain two-by-two block matrices with square blocks
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DOI: 10.1007/s10543-018-0741-x
Abstract: Two-by-two block matrices with square matrix blocks arise in many important applications. Since the problems are of large scale, iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is… read more here.
Keywords: two two; new version; two block; block matrices ... See more keywords
Parameter modified versions of preconditioning and iterative inner product free refinement methods for two-by-two block matrices
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DOI: 10.1016/j.laa.2019.07.024
Abstract: Abstract A special two-by-two block matrix form arises in many important applications. Extending earlier results it is shown that parameter modified versions of a very efficient preconditioner does not improve its rate of convergence. This… read more here.
Keywords: two two; modified versions; two block; parameter modified ... See more keywords
Dynamics of a nonlinear time-dependent two two-level atoms in a two-mode cavity
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DOI: 10.1142/s0219749920500033
Abstract: In this paper, we present some properties through two two-level atoms interacting with a two-mode quantized cavity field. We study this system in the presence of detuning parameter, Kerr nonlineari... read more here.
Keywords: two level; two mode; level atoms; two two ... See more keywords
A Two-by-Two matrix representation of a generalized Fibonacci sequence
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DOI: 10.15672/hjms.2017.477
Abstract: The Fibonacci sequence is a well-known example of second order recurrence sequence, which belongs to a particular class of recursive sequences. In this article, other generalized Fibonacci sequence is introduced and defined by $ H_{k,n+1}=2H_{k,n}+kH_{k,n-1},~n\geq1,~H_{k,0}=2,~H_{k,1}=1$… read more here.
Keywords: matrix representation; fibonacci sequence; generalized fibonacci; two two ... See more keywords