Connectionist models of memory storage have been studied for many years, and aim to provide insight into potential mechanisms of memory storage by the brain. A problem faced by these systems is that as the number of items to be stored increases across a finite set of neurons/synapses, the cumulative changes in synaptic weight eventually lead to a sudden and dramatic loss of the stored informati...

We present a novel distributed QR factorization algorithm for orthogonalizing a set of vectors in a decentralized wireless sensor network. The algorithm is based on the classical Gram-Schmidt orthogonalization with all projections and inner products reformulated in a recursive manner. In contrast to existing distributed orthogonalization algorithms, all elements of the resulting matrices Q and ...

Orthogonalization methods play a key role in many iterative methods. In this paper, we establish new properties for the modified Gram-Schmidt algorithm. We show why the modified Gram-Schmidt algorithm generates a well-conditioned set of vectors. This result holds under the assumption that the initial matrix is not “too ill-conditioned” in a way that is quantified. As a consequence we show that ...

In this note, we consider the modified Gram-Schmidt algorithm with reorthogonalization applied on a numerical nonsingular matrix, we explain why the resulting set of vectors is orthogonal up to the machine precision level. To establish this result, we show that a certain L-criterion is necessarily verified after the second reorthogonalization step, then we prove that this L-criterion implies th...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

Frames have turned out to be an essential tool for many applications such as, for example, data transmission, due to their robustness not only against noise but also against losses and due to their freedom in design [4, 6]. Their main advantage lies in the fact that a frame can be designed to be redundant while still providing a reconstruction formula. Since the frame operator Sg = ∑n i=1 〈g, f...

The representations currently used by local search and some evolutionary algorithms have the disadvantage that these algorithms are partially blind to “ridges” in the search space. Both heuristics search and gradient search algorithms can exhibit extremely slow convergence on functions that display ridge structures. A class of rotated representations are proposed and explored; these rotated rep...

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...

Mixed precision hardware has recently become commercially available, and more than 25% of the supercomputers in TOP500 list now have mixed capabilities. Using lower algorithms can be beneficial terms reducing both computation communication costs. There are many current efforts towards developing numerical linear algebra algorithms, which lead to speedups real applications. Motivated by this, we...