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Numerical-statistical projective estimates for solutions of integral equations are constructed and optimized using Legendre polynomials as motivated by the computational complexity of orthogonal expansions with an adapted weight. By applying analytical and corresponding numerical computations, the mean-square error is minimized as a function of the length of the projection expansion segment, while the sample size for the expansion coefficients is fixed. The proposed technique is successfully verified in a test problem close to the Milne one and is found to be more effective than the regularized expansion in terms of Laguerre polynomials. [ABSTRACT FROM AUTHOR]

The problem of minimizing the root-mean-square error of the numerical-statistical projection estimation of the solution to an integral equation is solved. It is shown that the optimal estimator in this sense can be obtained by equalizing deterministic and stochastic components of the error in the case when the norm of the remainder of the utilized decomposition decreases inversely proportional to its length. As a test, the Milne problem of radiation transfer in a semi-infinite layer of matter is solved using Laguerre polynomials. To solve such a problem in the case of a finite layer, a special regularized projection algorithm is used. [ABSTRACT FROM AUTHOR]

A comparative analysis of various projection Monte Carlo algorithms as applied to estimating the particle flow through a layer of medium with scattering of the Henyey–Greenstein type is carried out. The possibility of minimizing the mean-square error by equalizing the corresponding stochastic and deterministic terms is investigated. [ABSTRACT FROM AUTHOR]

We propose an on-line algorithm for exact filtering of multiple changepoint problems. This algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models. The computational cost of this exact algorithm is quadratic in the number of observations. We further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations, at the expense of introducing small errors, and we propose two new, optimum resampling algorithms for this problem. One, a version of rejection control, allows the particle filter to choose the number of particles that are required at each time step automatically. The new resampling algorithms substantially outperform standard resampling algorithms on examples that we consider; and we demonstrate how the resulting particle filter is practicable for segmentation of human G+C content. [ABSTRACT FROM AUTHOR]

The impingement disturbance characteristics of the hydrazine thruster plumes have been examined comprehensively for the ROCSAT-1 satellite. In this study, the velocity and temperature distributions at the nozzle exit are obtained from the nozzle flowfield analysis. The axial velocity, transverse velocity and temperature profiles are further correlated with the curve-fitting procedure for resolving inflow properties of molecules ejected into a vacuum. The free-molecular direct simulation M onte Carlo technique is used to describe the particle nature of the distant plume flow behaviour near the impingement surface. The inflow molecular motions as well as the collision interactions between the molecules and the solid surface are treated on a probabilistic basis. On the other hand, the intercollisions among molecules are considered to be relatively unimportant in the far-field plume region. A reasonable number of simulated molecules is also employed to reproduce the fluid behaviour in the macroscopic level. The predicted disturbance torques and thrust loss are found to be much less than the design control torques and the nominal thrust force for ROCSAT-1 satellite, indicating that the plume impingement effect will not cause any performance deterioration of the propulsive function. [ABSTRACT FROM AUTHOR]

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