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We address the semantic gap between the model and the implementation of control algorithms for distributed systems in a formal fashion: we provide an interactive (partially automated) method by which to translate the global, model level theoretical properties, such as stability and convergence, into code level assertions and invariants which assure termination of the relevant implementations and validity...
The 1980 IDR method plays an important role in the history of Krylov subspace methods. It started the research of transpose-free Krylov subspace methods. In this paper, we attempt to bring back A-transpose to the research by presenting a new ML(n)BiCGStab algorithm named ML(n)BiCGStabt. ML(n)BiCGStabt involves A-transpose in its implementation. Comparisons of this new algorithm with the existing ML(n)BiCGStab...
A stopping rule is developed for multidimensional stochastic approximation which seeks for a solution of an unknown equation based on random noise corrupted residuals. It is assumed that the equation is linear, and the noise is independent and identically distributed random vectors with a bounded covariance. Then, it is shown that the necessary number of iterations is bounded by a polynomial of the...
Let the observed sequence {yk} be generated by the multivariate ARMAX system A(z)yk = B(z)uk-1 + C(z)wk, where {wk} is the system noise with unknown covariance matrix Rw > 0, and {uk} is a sequence of mutually independent and identically distributed (iid) random vectors. Based on {yk} and {uk}, identification algorithms are proposed to simultaneously estimate the orders (p,q,r), the covariance...
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