T. Dayar and W. J. Stewart. On the effects of using the Grassmann-Taksar-Heyman method in iterative aggregation-disaggregation. SIAM J. Sci. Comput., 17:287--303, 1996  Home/Search   Document Details and Download   Summary   Related Articles   Check

No context found.

T. Dayar and W. J. Stewart. On the effects of using the Grassmann-Taksar-Heyman method in iterative aggregation-disaggregation. SIAM J. Sci. Comput., 17:287--303, 1996

....of states) and sparsity (i.e. tens of nonzeros per row) we consider the direct solution method of Grassmann Taksar Heyman (GTH) 8] at each level of Algorithm 1. This method is a more robust version of Gaussian elimination (GE) in which arithmetic with only positive numbers is performed [7]. We compare the run time of Algorithm 1 with that of GTH and IAD [18] which are both geared towards NCD MCs. In order to make a fair comparison, with IAD we use the same partitionings as in Algorithm 1. For all combinations of the integer parameters we considered, there is sufficient space to ....

T. Dayar, W.J. Stewart, On the effects of using the Grassmann-Taksar-Heyman method in iterative aggregation-disaggregation, SIAM Journal on Scientific Computing 17 (1996) 287--303.

....rows and columns of Q, and there is no difficulty in applying GTH to obtain an LU decomposition of either Q or Q T . Unfortunately, difficulties arise in implementing GTH when computer memory is at a premium and sparse compact storage schemes, such as those described in Section 3. 2, must be used [14]. Suppose first that Q is stored by rows and an LU decomposition of Q is sought. Both L and U need to be kept during the GTH reduction stage: the rows of U are needed to eliminate nonzero elements in the unreduced part of the coefficient matrix, while L is needed to compute the solution from L = ....

T. Dayar and W.J. Stewart. On the Effects of Using the Grassmann-Taksar-Heyman method in Iterative Aggregation-Disaggregation. SIAM Journal on Scientific Computing. Vol. 17, pp 1 - 17, 1996.

....and the partitionings, and the complete results. 2. Implementation Framework. In this study, we experiment with the (point) successive overrelaxation (SOR) method [30, 4] which is a stationary iterative method, two types of two level iterative methods, block SOR (BSOR) 30, 27, 22] and IAD [28, 32, 30, 11], and the Krylov subspace methods GMRES, DQGMRES, BCG, CGS, BCGStab, and QMR (see [4, 27] and the references therein) 2.1. Partitioning Techniques. When applied to NCD Markov chains, one possibility is to order and partition the state space so that the stochastic matrix of transition ....

T. Dayar and W. J. Stewart. On the effects of using the Grassmann-Taksar-Heyman method in iterative aggregation-disaggregation. SIAM J. Sci. Comput., 17, 287--303, 1996

....obligated to continue until the final operation has been performed. In this study, we experiment with the (point) successive overrelaxation (SOR) method [34, 4] a stationary iterative method. Moreover, two types of two level iterative methods are considered: block SOR (BSOR) 34, 28, 22] and IAD [36, 32, 34, 10]. As for projection techniques, we choose to implement and experiment with the Krylov subspace methods GMRES [29] DQGMRES [30] BCG [4] CGS [31] BCGStab [37] and QMR [12] 4 T. DAYAR and W. J. STEWART 2.1. Successive Over Relaxation (SOR) Stationary iterative methods are methods that can ....

....requires computing the stationary vector. This can be achieved by approximating the coupling matrix by starting with an approximate stationary vector and improving the approximate solution iteratively. The method motivated as such has come to be known as iterative aggregation disaggregation (IAD) [36, 32, 34, 10]. It is possible to perceive each iteration of the IAD algorithm as being formed of a preprocessing step followed by one iteration of a two level method, such as BSOR. The preprocessing step corresponds to the solution of the coupling matrix and is called aggregation. The BSOR iteration is the ....

[Article contains additional citation context not shown here]

T. Dayar and W. J. Stewart. On the effects of using the Grassmann-Taksar-Heyman method in iterative aggregation-disaggregation. SIAM J. Sci. Comput., 17:287--303, 1996

No context found.

T. Dayar and W. J. Stewart. On the effects of using the GrassmannTaksar -Heyman method in iterative aggregation-disaggregation. SIAM J. Sci. Comput., 17(1):287--303, January 1996.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC