The problem of finding the optimal set of quantized coefficients for a frame-based encoded signal is known to be of very high complexity. This paper presents an efficient method of finding the operational Rate-Distortion (RD) optimal set of coefficients. The major complexity reduction lies in the reformulation of the original RD-tradeoff problem, where a new set of coefficients is used as decis...

An analytical approach to the performance analysis of the V-BLAST algorithm is discussed in this paper. It is based on closed-form analytical models of the three key algorithm components: interference cancellation, interference nulling and optimal ordering. The closed-form analytical model of the GramSchmidt orthogonalization process is a key component of the proposed analysis method. It allows...

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt...

Selected Common Threads and Root Concepts Linking Old to New Sandra L. Arlinghaus* and Joseph Kerski** Introduction In the twentieth century, much of mathematics experienced a well-known paradigm shift in moving from a focus on mathematical objects to a focus on transformations of objects. Thus, one sees, for example, linear algebra courses that focus on matrix vector products as linear transfo...

It is known that the restarted full orthogonalization method (FOM) outperforms the restarted generalized minimum residual method (GMRES) in several circumstances for solving shifted linear systems when the shifts are handled simultaneously. On the basis of theWeightedArnoldi process, aweighted version of the Restarted Shifted FOM is proposed, which can provide accelerating convergence rate with...

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the contr...

By the example of a mathematical model of a biochemical process, the structural instability of dynamical systems is studied by calculating the full spectrum of Lyapunov indices with the use of the generalized Benettin algorithm. For the reliability of the results obtained, the higher Lyapunov index determined with the orthogonalization of perturbation vectors by the Gram– Schmidt method is comp...

A general expression for the distortion rate function (DRF) of cyclostationary Gaussian processes in terms of their spectral properties is derived. This expression can be seen as the result of orthogonalization over the different components in the polyphase decomposition of the process. We use this expression to derive, in a closed form, the DRF of several cyclostationary processes arising in p...

A highly parallelizable domain decomposition solution technique for adaptive hp finite element methods is developed. The technique uses good partitioning strategies and a subspace decomposition based preconditioned iterative solver, Two level orthogonalization is used to obtain a reduced system which is preconditioned by a coarse grid operator. Numerical results show fast cOIl\'ergence for the ...