Uniform approximation of wave functions with improved semiclassical transformation amplitudes and Gram-Schmidt orthogonalization

Experiments on Gram-schmidt Orthogonalization

(3) In addition to solutions for | k | ^ 9999, we have solutions, for y ^ 104 and | k | g 99999; there are 1221 for positive k and 799 for negative k. The vast majority of solutions are with y < 100 and Table 2 gives the number of solutions for various ranges of y. The fact that the number of solutions is a rapidly decreasing function of y suggests that for at least some k the solution set may ...

Gram-Schmidt orthogonalization: 100 years and more

Gram – Schmidt Orthogonalization on Encrypted Vectors

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...

Multiple Description Quantization via Gram-Schmidt Orthogonalization

The multiple description (MD) problem has received considerable attention as a model of information transmission over unreliable channels. A general framework for designing efficient multiple description quantization schemes is proposed in this paper. We provide a systematic treatment of the El Gamal-Cover (EGC) achievable MD rate-distortion region, and show that any point in the EGC region can...

Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement

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 ...