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 ...

In this paper, we compare with the inverse iteration algorithms on PowerXCell 8i processor, which has been known as a heterogeneous environment. When some of all the eigenvalues are close together or there are clusters of eigenvalues, reorthogonalization must be adopted to all the eigenvectors associated with such eigenvalues. Reorthogonalization algorithms need a lot of computational cost. The...

In this paper we address a privacy preserving version of the well known Gram – Schmidt Orthogonalization procedure. Specifically, we propose a building block for secure multiparty computation, that is able to orthogonalize a set of componentwise encrypted vectors. Our setting is the following: Bob needs to compute this orthogonalization on some vectors encrypted with the public key of Alice. He...

The construction of distributed algorithms for matrix computations built on top of distributed data aggregation algorithms with randomized communication schedules is investigated. For this purpose, a new aggregation algorithm for summing or averaging distributed values, the push-flow algorithm, is developed, which achieves superior resilience properties with respect to failures compared to exis...

This paper describes the use of orthogonal space-time block codes to overcome the performance and complexity difficulties associated with the use of Shaped Offset QPSK (SOQPSK) modulation, a ternary continuous phase modulation (CPM), in multiple-input multiple-output telemetry systems. The orthogonal space-time block code is applied to SOQPSK waveforms in the same way it would be applied to sym...

We propose a mixed-precision orthogonalization scheme that takes the input matrix in a standard 32 or 64-bit floating-point precision, but uses higher-precision arithmetics to accumulate its intermediate results. For the 64-bit precision, our scheme uses software emulation for the higher-precision arithmetics, and requires about 20× more computation but about the same amount of communication as...

A new orthogonalization technique is presented for computing the QR factorization of a general n X p matrix of full rank p (n > p). The method is based on the use of projections to solve increasingly larger subproblems recursively and has an 0(np2) operation count for general matrices. The technique is readily adaptable to solving linear least-squares problems. If the initial matrix has a circu...

Convergence acceleration by preconditioning is usually essential when solving the standard least squares problems by an iterative method. IMGS, is an incomplete modiied version of Gram-Schmidt orthogonalization to obtain an incomplete orthogonal factorization pre-conditioner M = R, where A = Q R + E is an approximation of a QR factorization, Q is an orthogonal matrix and R is upper triangular m...

A computationally efficient analytic form of the Born-approximation electron-impact ionization amplitude is derived for general neutral-atom targets. High-quality Hartree-Fock Slater orbitals are used to model the target wave function. Full orthogonalization of the continuum Coulomb wave to all occupied orbitals of the target atom is enforced. Results are presented for noble gases ~Ne, Ar, Kr, ...

A new transformation is proposed that gives orthogonal components with a one-to-one correspondence between the original vectors and the components. The aim is that each component should be close to the vector with which it is paired, orthogonality imposing a constraint. If the vectors have been normalized, then the transformation minimizes the sum of the squared correlations between each vector...