Результаты поиска по 'LD factorization':
Найдено статей: 2
  1. Tsyganova J.V., Tsyganov A.V.
    LD filter for the state estimation of pairwise Markov models
    Computer Research and Modeling, 2026, v. 18, no. 4, pp. 747-764

    The paper addresses the state estimation problem for pairwise Markov models with Gaussian noises. The class of pairwise Markov models generalizes the classical hidden Markov models. The key difference lies in the assumption that the Markov property holds not for the hidden process alone, but for the pair consisting of the state and the observation. This allows modeling more complex dependencies and, in particular, eliminates the requirement of Markovianity for the hidden process. For linear Gaussian pairwise models, Kalman filtering methods remain applicable, leading to the concept of the pairwise Kalman filter.

    This work proposes a new modification of the pairwise Kalman filter based on the application of modified weighted Gram – Schmidt orthogonalization and the LD decomposition of covariance matrices. The main results are as follows: a novel LD modification of the pairwise Kalman filter (Theorem 1); a new LD-PKF algorithm for state estimation of pairwise Markov models, based on a direct procedure of modified weighted Gram–Schmidt orthogonalization and LD decomposition of covariance matrices (algorithm 2); results of comparative analysis on the numerical properties of pairwise discrete filtering algorithms.

    The obtained theoretical results complement the theory of pairwise filtering in the class of linear discrete pairwise Markov models with Gaussian noises.

    The developed algorithm is implemented in MATLAB. A series of numerical experiments are conducted, and the results demonstrate its effectiveness and numerical advantages over other existing modifications of the pairwise Kalman filter.

    The presented results can be further used to develop new methods for parameter identification of pairwise Markov models.

    Keywords: pairwise Markov model, pairwise Kalman filter, MWGS orthogonalization, LD factorization, discrete-time filtering algorithm.
  2. Zhmurov A.A., Barsegov V.A., Trifonov S.V., Kholodov Y.A., Kholodov A.S.
    Efficient Pseudorandom number generators for biomolecular simulations on graphics processors
    Computer Research and Modeling, 2011, v. 3, no. 3, pp. 287-308

    Langevin Dynamics, Monte Carlo, and all-atom Molecular Dynamics simulations in implicit solvent require a reliable source of pseudorandom numbers generated at each step of calculation. We present the two main approaches for implementation of pseudorandom number generators on a GPU. In the first approach, inherent in CPU-based calculations, one PRNG produces a stream of pseudorandom numbers in each thread of execution, whereas the second approach builds on the ability of different threads to communicate, thus, sharing random seeds across the entire device. We exemplify the use of these approaches through the development of Ran2, Hybrid Taus, and Lagged Fibonacci algorithms. As an application-based test of randomness, we carry out LD simulations of N independent harmonic oscillators coupled to a stochastic thermostat. This model allows us to assess statistical quality of pseudorandom numbers. We also profile performance of these generators in terms of the computational time, memory usage, and the speedup factor (CPU/GPU time).

    Keywords: GPU, pseudorandom numbers, PRNG, biomolecules.
    Views (last year): 11. Citations: 2 (RSCI).

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