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 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...

Empirical mode decomposition (EMD) and Empirical wavelet transform (EWT) are recently developed adaptive signal processing tools. These techniques decompose a signal accordingly to its contained information. The main issue with EMD is its lack of theory and in case of EWT a prior knowledge of the signal is required. IMF’s obtained as a result of applying EMD are quasi-orthogonal .This paper sug...

Important operations in numerical computing are vector orthogonalization. One of the well-known algorithms for vector orthogonalisation is Gram–Schmidt algorithm. This is a method for constructing a set of orthogonal vectors in an inner product space, most commonly the Euclidean space Rn. This process takes a finite, linearly independent set S = {b1, b2, ..., bk} vectors for k ≤ n and generates...

We study decompositions of functions in the Hardy spaces into linear combinations of the basic functions in the orthogonal rational systems {Bn(x)} which can be obtained in the respective contexts through Gram-Schmidt orthogonalization process on shifted Cauchy kernels. Those lead to adaptive decompositions of quaternionic-valued signals of finite energy. This study is a generalization of the m...

K e y w o r d s N u m e r i c a l linear algebra, QR factorization, Gram-Schmidt orthogonalization, Reorthogonalization, Rounding error analysis. 1. I N T R O D U C T I O N Scientific comput ing and ma themat i ca l models in engineering are becoming increasingly dependent upon development and implementa t ion of efficient paral le l a lgor i thms on modern high performance computers . Numerica...

Various methods of constructing an orthonomal set out of a given set of linearly independent vectors are discussed. Particular attention is paid to the Gram-Schmidt and the Schweinler-Wigner orthogonalization procedures. A new orthogonalization procedure which, like the SchweinlerWigner procedure, is democratic and is endowed with an extremal property is suggested. PACS No: 02.10.Sp, 31.15.+q e...