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Iterative Methods

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Book cover Analyzing Markov Chains using Kronecker Products

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Abstract

Classical iterative methods for the solution of a linear system of equations as in (1.3) start with an initial approximation. At each iteration, they multiply the current approximation with a particular matrix to obtain a new approximation with the objective that the approximations eventually converge to the true solution [83, 130]. These methods are the building blocks of all advanced iterative methods. The matrix used in the iterative multiplication process is obtained at the outset by splitting the coefficient matrix of the linear system, which is Q in our setting. Therefore, we begin by splitting the smaller matrices that form the Kronecker products as in [146] and show how classical iterative methods can be formulated in terms of these smaller matrices.

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    Tuğrul Dayar

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Dayar, T. (2012). Iterative Methods. In: Analyzing Markov Chains using Kronecker Products. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4190-8_3

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