scholarly journals Eigenvalue Estimates via Pseudospectra

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1729
Author(s):  
Georgios Katsouleas ◽  
Vasiliki Panagakou ◽  
Panayiotis Psarrakos
Keyword(s):  
Complex Plane ◽  
Large Scale ◽  
Matrix Polynomial ◽  
Parallel Implementation ◽  
Boundary Curve ◽  
Recursive Procedure ◽  
Eigenvalue Estimates ◽  
General Matrix ◽  
Initial Term ◽  
Grid Algorithms

In this note, given a matrix A∈Cn×n (or a general matrix polynomial P(z), z∈C) and an arbitrary scalar λ0∈C, we show how to define a sequence μkk∈N which converges to some element of its spectrum. The scalar λ0 serves as initial term (μ0=λ0), while additional terms are constructed through a recursive procedure, exploiting the fact that each term μk of this sequence is in fact a point lying on the boundary curve of some pseudospectral set of A (or P(z)). Then, the next term in the sequence is detected in the direction which is normal to this curve at the point μk. Repeating the construction for additional initial points, it is possible to approximate peripheral eigenvalues, localize the spectrum and even obtain spectral enclosures. Hence, as a by-product of our method, a computationally cheap procedure for approximate pseudospectra computations emerges. An advantage of the proposed approach is that it does not make any assumptions on the location of the spectrum. The fact that all computations are performed on some dynamically chosen locations on the complex plane which converge to the eigenvalues, rather than on a large number of predefined points on a rigid grid, can be used to accelerate conventional grid algorithms. Parallel implementation of the method or use in conjunction with randomization techniques can lead to further computational savings when applied to large-scale matrices.

scholarly journals A Parallel Unmixing-Based Content Retrieval System for Distributed Hyperspectral Imagery Repository on Cloud Computing Platforms

2021 ◽  
Vol 13 (2) ◽  
pp. 176
Author(s):  
Peng Zheng ◽  
Zebin Wu ◽  
Jin Sun ◽  
Yi Zhang ◽  
Yaoqin Zhu ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Large Scale ◽  
Retrieval System ◽  
Hyperspectral Image ◽  
Parallel Implementation ◽  
Remotely Sensed Data ◽  
Web Interfaces ◽  
Content Retrieval ◽  
Service Mode ◽  
Computing Platforms

As the volume of remotely sensed data grows significantly, content-based image retrieval (CBIR) becomes increasingly important, especially for cloud computing platforms that facilitate processing and storing big data in a parallel and distributed way. This paper proposes a novel parallel CBIR system for hyperspectral image (HSI) repository on cloud computing platforms under the guide of unmixed spectral information, i.e., endmembers and their associated fractional abundances, to retrieve hyperspectral scenes. However, existing unmixing methods would suffer extremely high computational burden when extracting meta-data from large-scale HSI data. To address this limitation, we implement a distributed and parallel unmixing method that operates on cloud computing platforms in parallel for accelerating the unmixing processing flow. In addition, we implement a global standard distributed HSI repository equipped with a large spectral library in a software-as-a-service mode, providing users with HSI storage, management, and retrieval services through web interfaces. Furthermore, the parallel implementation of unmixing processing is incorporated into the CBIR system to establish the parallel unmixing-based content retrieval system. The performance of our proposed parallel CBIR system was verified in terms of both unmixing efficiency and accuracy.

scholarly journals Parallel Framework for Dimensionality Reduction of Large-Scale Datasets

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sai Kiranmayee Samudrala ◽  
Jaroslaw Zola ◽  
Srinivas Aluru ◽  
Baskar Ganapathysubramanian
Keyword(s):  
Dimensionality Reduction ◽  
Organic Solar Cells ◽  
Large Scale ◽  
Parallel Implementation ◽  
High Dimensional Data ◽  
Real Life ◽  
Processing Parameters ◽  
High Dimensional ◽  
Morphology Evolution ◽  
Reduction Techniques

Dimensionality reduction refers to a set of mathematical techniques used to reduce complexity of the original high-dimensional data, while preserving its selected properties. Improvements in simulation strategies and experimental data collection methods are resulting in a deluge of heterogeneous and high-dimensional data, which often makes dimensionality reduction the only viable way to gain qualitative and quantitative understanding of the data. However, existing dimensionality reduction software often does not scale to datasets arising in real-life applications, which may consist of thousands of points with millions of dimensions. In this paper, we propose a parallel framework for dimensionality reduction of large-scale data. We identify key components underlying the spectral dimensionality reduction techniques, and propose their efficient parallel implementation. We show that the resulting framework can be used to process datasets consisting of millions of points when executed on a 16,000-core cluster, which is beyond the reach of currently available methods. To further demonstrate applicability of our framework we perform dimensionality reduction of 75,000 images representing morphology evolution during manufacturing of organic solar cells in order to identify how processing parameters affect morphology evolution.

scholarly journals The large-scale blast score ratio (LS-BSR) pipeline: a method to rapidly compare genetic content between bacterial genomes

2014 ◽  
Author(s):  
Jason W Sahl ◽  
Greg Caporaso ◽  
David A Rasko ◽  
Paul S Keim
Keyword(s):  
Large Scale ◽  
Sequence Data ◽  
Parallel Implementation ◽  
Genetic Relationships ◽  
Clinical Diagnostics ◽  
Whole Genome Sequence ◽  
Bacterial Isolates ◽  
Bacterial Genomes ◽  
E Coli ◽  
Blast Score

Background. As whole genome sequence data from bacterial isolates becomes cheaper to generate, computational methods are needed to correlate sequence data with biological observations. Here we present the large-scale BLAST score ratio (LS-BSR) pipeline, which rapidly compares the genetic content of hundreds to thousands of bacterial genomes, and returns a matrix that describes the relatedness of all coding sequences (CDSs) in all genomes surveyed. This matrix can be easily parsed in order to identify genetic relationships between bacterial genomes. Although pipelines have been published that group peptides by sequence similarity, no other software performs the large-scale, flexible, full-genome comparative analyses carried out by LS-BSR. Results. To demonstrate the utility of the method, the LS-BSR pipeline was tested on 96 Escherichia coli and Shigella genomes; the pipeline ran in 163 minutes using 16 processors, which is a greater than 7-fold speedup compared to using a single processor. The BSR values for each CDS, which indicate a relative level of relatedness, were then mapped to each genome on an independent core genome single nucleotide polymorphism (SNP) based phylogeny. Comparisons were then used to identify clade specific CDS markers and validate the LS-BSR pipeline based on molecular markers that delineate between classical E. coli pathogenic variant (pathovar) designations. Scalability tests demonstrated that the LS-BSR pipeline can process 1,000 E. coli genomes in ~60h using 16 processors. Conclusions. LS-BSR is an open-source, parallel implementation of the BSR algorithm, enabling rapid comparison of the genetic content of large numbers of genomes. The results of the pipeline can be used to identify specific markers between user-defined phylogenetic groups, and to identify the loss and/or acquisition of genetic information between bacterial isolates. Taxa-specific genetic markers can then be translated into clinical diagnostics, or can be used to identify broadly conserved putative therapeutic candidates.

Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems

2008 ◽  
pp. 227-234 ◽  
Author(s):  
Jose M. Badía ◽  
Peter Benner ◽  
Rafael Mayo ◽  
Enrique S. Quintana-Ortí ◽  
Gregorio Quintana-Ortí ◽  
...  
Keyword(s):  
Large Scale ◽  
Parallel Implementation ◽  
Balanced Truncation ◽  
Large Scale Systems

Assembling of Parallel Programs for Large Scale Numerical Modeling

2012 ◽  
pp. 497-511
Author(s):  
V.E. Malyshkin
Keyword(s):  
Large Scale ◽  
Parallel Implementation ◽  
Numerical Models ◽  
Dynamic Properties ◽  
Parallel Program ◽  
Particle In Cell ◽  
Modular Programming ◽  
Rectangular Mesh ◽  
Assembly Technology ◽  
Main Ideas

The main ideas of the Assembly Technology (AT) in its application to parallel implementation of large scale realistic numerical models on a rectangular mesh are considered and demonstrated by the parallelization (fragmentation) of the Particle-In-Cell method (PIC) application to solution of the problem of energy exchange in plasma cloud. The implementation of the numerical models with the assembly technology is based on the construction of a fragmented parallel program. Assembling of a numerical simulation program under AT provides automatically different useful dynamic properties of the target program including dynamic load balance on the basis of the fragments migration from overloaded into underloaded processor elements of a multicomputer. Parallel program assembling approach also can be considered as combination and adaptation for parallel programming of the well known modular programming and domain decomposition techniques and supported by the system software for fragmented programs assembling.

A Boundary Element Method for Plane Anisotropic Elastic Media

1990 ◽  
Vol 57 (3) ◽  
pp. 600-606 ◽  
Author(s):  
Kyu J. Lee ◽  
A. K. Mal
Keyword(s):  
Integral Equations ◽  
Complex Plane ◽  
Singular Integral Equations ◽  
Boundary Curve ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Numerical Formulation ◽  
Complex Linear ◽  
Anisotropic Elastic ◽  
Improved Accuracy

The general problem of plane anisotropic elastostatics is formulated in terms of a system of singular integral equations with Cauchy kernels by means of the classical stress function approach. The integral equations are represented over the image of the boundary in the complex plane and a numerical scheme is developed for their solution. The boundary curve is discretized and suitable polynomial approximations of the unknown functions in terms of the complex variable are introduced. This reduces the equations to a set of complex linear algebraic equations which can be inverted to yield the stresses in a straightforward manner. The major difference between the present technique and the previous ones is in the numerical formulation. The integral equations are discretized in the complex plane and not in terms of real variables which depend on arc length, resulting in improved accuracy in presence of strong boundary curvature.

PARALLEL AGENT-BASED SIMULATION ON A CLUSTER OF WORKSTATIONS

2003 ◽  
Vol 13 (04) ◽  
pp. 629-641 ◽  
Author(s):  
Konstantin Popov ◽  
Mahmoud Rafea ◽  
Fredrik Holmgren ◽  
Per Brand ◽  
Vladimir Vlassov ◽  
...  
Keyword(s):  
Web Sites ◽  
Large Scale ◽  
Parallel Implementation ◽  
Simulation Models ◽  
Agent Based Simulation ◽  
Time Step ◽  
Agent Based ◽  
Simulation Step ◽  
Cluster Of Workstations ◽  
Concurrent Simulation

We discuss a parallel implementation of an agent-based simulation. Our approach allows to adapt a sequential simulator for large-scale simulation on a cluster of workstations. We target discrete-time simulation models that capture the behavior of Web users and Web sites. Web users are connected with each other in a graph resembling the social network. Web sites are also connected in a similar graph. Users are stateful entities. At each time step, they exhibit certain behaviour such as visiting bookmarked sites, exchanging information about Web sites in the "word-of-mouth" style, and updating bookmarks. The real-world phenomena of emerged aggregated behavior of the Internet population is studied. The system distributes data among workstations, which allows large-scale simulations infeasible on a stand-alone computer. The model properties cause traffic between workstations proportional to partition sizes. Network latency is hidden by concurrent simulation of multiple users. The system is implemented in Mozart that provides multithreading, dataflow variables, component-based software development, and network-transparency. Currently we can simulate up to 106 Web users on 104 Web sites using a cluster of 16 computers, which takes few seconds per simulation step, and for a problem of the same size, parallel simulation offers speedups between 11 and 14.

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