12,750 research outputs found
Matrix Shanks Transformations
Shanks' transformation is a well know sequence transformation for accelerating the convergence of scalar sequences. It has been extended to the case of sequences of vectors and sequences of square matrices satisfying a linear difference equation with scalar coefficients. In this paper, a more general extension to the matrix case where the matrices can be rectangular and satisfy a difference equation with matrix coefficients is proposed and studied. In the particular case of square matrices, the new transformation can be recursively implemented by the matrix -algorithm of Wynn. Then, the transformation is related to matrix Pad\ue9-type and Pad\ue9 approximants. Numerical experiments showing the interest of this transformation end the paper
Quantum line bundles on noncommutative sphere
Noncommutative (NC) sphere is introduced as a quotient of the enveloping
algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we
introduce projective modules which are analogues of line bundles on the usual
sphere (we call them quantum line bundles) and define a multiplicative
structure in their family. Also, we compute a pairing between certain quantum
line bundles and finite dimensional representations of the NC sphere in the
spirit of the NC index theorem. A new approach to constructing the differential
calculus on a NC sphere is suggested. The approach makes use of the projective
modules in question and gives rise to a NC de Rham complex being a deformation
of the classical one.Comment: LaTeX file, 15 pp, no figures. Some clarifying remarks are added at
the beginning of section 2 and into section
Communication-Avoiding Optimization Methods for Distributed Massive-Scale Sparse Inverse Covariance Estimation
Across a variety of scientific disciplines, sparse inverse covariance
estimation is a popular tool for capturing the underlying dependency
relationships in multivariate data. Unfortunately, most estimators are not
scalable enough to handle the sizes of modern high-dimensional data sets (often
on the order of terabytes), and assume Gaussian samples. To address these
deficiencies, we introduce HP-CONCORD, a highly scalable optimization method
for estimating a sparse inverse covariance matrix based on a regularized
pseudolikelihood framework, without assuming Gaussianity. Our parallel proximal
gradient method uses a novel communication-avoiding linear algebra algorithm
and runs across a multi-node cluster with up to 1k nodes (24k cores), achieving
parallel scalability on problems with up to ~819 billion parameters (1.28
million dimensions); even on a single node, HP-CONCORD demonstrates
scalability, outperforming a state-of-the-art method. We also use HP-CONCORD to
estimate the underlying dependency structure of the brain from fMRI data, and
use the result to identify functional regions automatically. The results show
good agreement with a clustering from the neuroscience literature.Comment: Main paper: 15 pages, appendix: 24 page
Memory architecture
A memory architecture is presented. The memory architecture comprises a first memory and a second memory. The first memory has at least a bank with a first width addressable by a single address. The second memory has a plurality of banks of a second width, said banks being addressable by components of an address vector. The second width is at most half of the first width. The first memory and the second memory are coupled selectively and said first memory and second memory are addressable by an address space. The invention further provides a method for transposing a matrix using the memory architecture comprising following steps. In the first step the matrix elements are moved from the first memory to the second memory. In the second step a set of elements arranged along a warped diagonal of the matrix is loaded into a register. In the fourth step the set of elements stored in the register are rotated until the element originating from the first row of the matrix is in a first location of the register. In the fifth step the rotated set of elements are stored in the second memory to obtain a transposed warped diagonal. The second to fifth steps are repeated with the subsequent warp diagonals until matrix transposition is complete
Phase matrix induced symmetrics for multiple scattering using the matrix operator method
Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable
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