• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.59-80
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• 2003

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are form to solve linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed implicitly. A diagonal perturbation strategy is implemented to enhance factorization robustness. The factors obtained are used as a preconditioner for the conjugate gradient method. Numerical experiments are used to show the robustness and efficiency of this preconditioning technique, and to compare it with two other preconditioners.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.560-570
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• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• Journal of the Korea Society of Computer and Information
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• v.11 no.3
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• pp.141-149
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• 2006

In this paper, we introduce an improved algorithm for computing matrix triple product that commonly arises in primal-dual optimization method. In computing $P=AHA^{t}$, we devise a single pass algorithm that exploits the block diagonal structure of the matrix H. This one-phase scheme requires fewer floating point operations and roughly half the memory of the generic two-phase algorithm, where the product is computed in two steps, computing first $Q=HA^{t}$ and then P=AQ. The one-phase scheme achieved speed-up of 2.04 on Intel Itanium II platform over the two-phase scheme. Based on memory latency and modeled cache miss rates, the performance improvement was evaluated through performance modeling. Our research has impact on performance tuning study of complex sparse matrix operations, while most of the previous work focused on performance tuning of basic operations.