Vector orthogonal relations. Vector QD-algorithm

Stieltjes continued fraction and QD algorithm; scalar, vector, matrix cases.

Orthogonal Vector Computations

Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.

Orthogonal Vector Coloring

A vector coloring of a graph is an assignment of a vector to each vertex where the presence or absence of an edge between two vertices dictates the value of the inner product of the corresponding vectors. In this paper, we obtain results on orthogonal vector coloring, where adjacent vertices must be assigned orthogonal vectors. We introduce two vector analogues of list coloring along with their...

Lapped Orthogonal Vector Quantization

The block processing inherent in the use of traditional vector quantization (VQ) schemes typically gives rise to perceptually distracting blocking artifacts. We demonstrate that such artifacts can, in general, be virtually eliminated via an e cient lapped VQ strategy. With lapped VQ schemes, blocks are obtained from the source in an overlapped manner, and reconstructed via superposition of over...

Implementation of the Orthogonal QD Algorithm for Lower Tridiagonal Matrices

The orthogonal qd algorithm with shifts (oqds algorithm), proposed by von Matt, is an algorithm for computing the singular values of bidiagonal matrices. This algorithm is accurate in terms of relative error, and it is also applicable to general triangular matrices. In particular, for lower tridiagonal matrices, BLAS Level 2.5 routines are available in preprocessing stage for this algorithm. BL...