scholarly journals On the Efficiency of Algorithms with Multi-level Parallelism

2021 ◽  
pp. 133-137
Author(s):  
Oleksandr Popov ◽  
Oleksiy Chystiakov
Keyword(s):  
Parallel Computing ◽  
Multilevel Model ◽  
Hybrid Architecture ◽  
Positive Definite Matrices ◽  
Computational Mathematics ◽  
Mathematics Problems ◽  
Efficiency Of Algorithms ◽  
Multi Level ◽  
Symmetric Positive Definite Matrices ◽  
Level Parallelism

The paper investigates the efficiency of algorithms for solving computational mathematics problems that use a multilevel model of parallel computing on heterogeneous computer systems. A methodology for estimating the acceleration of algorithms for computers using a multilevel model of parallel computing is proposed. As an example, the parallel algorithm of the iteration method on a subspace for solving the generalized algebraic problem of eigenvalues of symmetric positive definite matrices of sparse structure is considered. For the presented algorithms, estimates of acceleration coefficients and efficiency were obtained on computers of hybrid architecture using graphics accelerators, on multi-core computers with shared memory and multi-node computers of MIMD-architecture.

scholarly journals The design and evaluation of hierarchical multi-level parallelisms for H.264 encoder on multi-core architecture

2010 ◽  
Vol 7 (1) ◽  
pp. 189-200 ◽  
Author(s):  
Haitao Wei ◽  
Yu Junqing ◽  
Li Jiang
Keyword(s):  
Video Coding ◽  
Experimental Results ◽  
Bit Rate ◽  
Low Bit Rate ◽  
Good Compromise ◽  
Multi Level ◽  
Level Parallelism ◽  
Data Level ◽  
Intel Xeon

As a video coding standard, H.264 achieves high compress rate while keeping good fidelity. But it requires more intensive computation than before to get such high coding performance. A Hierarchical Multi-level Parallelisms (HMLP) framework for H.264 encoder is proposed which integrates four level parallelisms - frame-level, slice-level, macroblock-level and data-level into one implementation. Each level parallelism is designed in a hierarchical parallel framework and mapped onto the multi-cores and SIMD units on multi-core architecture. According to the analysis of coding performance on each level parallelism, we propose a method to combine different parallel levels to attain a good compromise between high speedup and low bit-rate. The experimental results show that for CIF format video, our method achieves the speedup of 33.57x-42.3x with 1.04x-1.08x bit-rate increasing on 8-core Intel Xeon processor with SIMD Technology.

A Trace Inequality for Symmetric Nonnegative Definite Matrices

2011 ◽  
Vol 225-226 ◽  
pp. 970-973
Author(s):  
Shi Qing Wang
Keyword(s):  
Control Theory ◽  
Communication Systems ◽  
Positive Definite ◽  
Trace Inequality ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Multiple Input ◽  
Nonnegative Definite ◽  
Symmetric Positive Definite Matrices ◽  
Trace Inequalities

Trace inequalities naturally arise in control theory and in communication systems with multiple input and multiple output. One application of Belmega’s trace inequality has already been identified [3]. In this paper, we extend the symmetric positive definite matrices of his inequality to symmetric nonnegative definite matrices, and the inverse matrices to Penrose-Moore inverse matrices.

Geometric two-scale convergence on forms and its applications to Maxwell's equations

2005 ◽  
Vol 135 (1) ◽  
pp. 133-147 ◽  
Author(s):  
Hee Chul Pak
Keyword(s):  
Maxwell Equations ◽  
Differential Forms ◽  
Random Coefficients ◽  
Parabolic Partial Differential Equation ◽  
Positive Definite Matrices ◽  
Partial Differential ◽  
Second Order Elliptic Equation ◽  
Image Position ◽  
Symmetric Positive Definite Matrices ◽  
Well Posed

We develop the geometric two-scale convergence on forms in order to describe the homogenization of partial differential equations with random variables on non-flat domain. We prove the compactness theorem and some two-scale behaviours for differential forms. For its applications, we investigate the limiting equations of the n-dimensional Maxwell equations with random coefficients, with given initial and boundary conditions, where are symmetric positive-definite matrices for x ∈ M, and M is an n-dimensional compact oriented Riemannian manifold with smooth boundary. The limiting system of n-dimensional Maxwell equations turns out to be degenerate and it is proven to be well-posed. The homogenized coefficients affected by the geometry of the domain are presented, and compared with the homogenized coefficient of the second order elliptic equation. We present the convergence theorem in order to explain the convergence of the solutions of Maxwell system as a parabolic partial differential equation.

Exploring Multi-level Parallelism in Cellular Automata Networks

2000 ◽  
pp. 336-343 ◽  
Author(s):  
Claudia Roberta Calidonna ◽  
Claudia Di Napoli ◽  
Maurizio Giordano ◽  
Mario Mango Furnari
Keyword(s):  
Cellular Automata ◽  
Automata Networks ◽  
Multi Level ◽  
Level Parallelism

scholarly journals EEG representation using multi-instance framework on the manifold of symmetric positive definite matrices

2019 ◽  
Vol 16 (3) ◽  
pp. 036016 ◽  
Author(s):  
Khadijeh Sadatnejad ◽  
Mohammad Rahmati ◽  
Reza Rostami ◽  
Reza Kazemi ◽  
Saeed S Ghidary ◽  
...  
Keyword(s):  
Positive Definite ◽  
Positive Definite Matrices ◽  
Symmetric Positive Definite ◽  
Symmetric Positive Definite Matrices
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