scholarly journals A combined direct-iterative approach for solving large scale singular and rectangular consistent systems of linear equations

1980 ◽  
Vol 34 ◽  
pp. 85-101 ◽  
Author(s):  
M. Neumann
Keyword(s):  
Large Scale ◽  
Linear Equations ◽  
Iterative Approach ◽  
Systems Of Linear Equations

scholarly journals New Algorithms for Secure Outsourcing of Large-Scale Systems of Linear Equations

2020 ◽  
Vol 9 (5) ◽  
pp. 545-550
Keyword(s):  
Cloud Computing ◽  
Distributed Computing ◽  
Data Storage ◽  
Large Scale ◽  
Homomorphic Encryption ◽  
Linear Equations ◽  
Force Transmission ◽  
Large Scale Systems ◽  
Secure Outsourcing ◽  
Systems Of Linear Equations

Cloud computing is the on-request accessibility of computer system resources, specially data storage and computing power, without direct dynamic management by the client. In the simplest terms, cloud computing means storing and accessing data and programs over the Internet instead of your computer’s hard drive. Along the improvement of cloud computing, more and more applications are migrated into the cloud. A significant element of distributed computing is pay-more only as costs arise. Distributed computing gives strong computational capacity to the general public at diminished cost that empowers clients with least computational assets to redistribute their huge calculation outstanding burdens to the cloud, and monetarily appreciate the monstrous computational force, transmission capacity, stockpiling, and even reasonable programming that can be partaken in a compensation for each utilization way Tremendous bit of leeway is the essential objective that forestalls the wide scope of registering model for clients when their secret information are expended during the figuring procedure. Critical thinking is a system to arrive at the pragmatic objective of specific instruments that tackles the issues as well as shield from pernicious practices.. In this paper, we examine secure outsourcing for large-scale systems of linear equations, which are the most popular problems in various engineering disciplines. Linear programming is an operation research technique formulates private data by the customer for LP problem as a set of matrices and vectors, to develop a set of efficient privacypreserving problem transformation techniques, which allow customers to transform original LP problem into some arbitrary one while protecting sensitive input/output information. Identify that LP problem solving in Cloud component is efficient extra cost on cloud server. In this paper we are utilizing Homomorphic encryption system to increase the performance and time efficiency

scholarly journals Accelerating advanced preconditioning methods on hybrid architectures

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Ernesto Dufrechou
Keyword(s):  
Linear Systems ◽  
Large Scale ◽  
Krylov Subspace ◽  
Linear Equations ◽  
Memory Systems ◽  
Sparse Linear Systems ◽  
Data Parallel ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Computational Bottleneck

Many problems, in diverse areas of science and engineering, involve the solution of largescale sparse systems of linear equations. In most of these scenarios, they are also a computational bottleneck, and therefore their efficient solution on parallel architectureshas motivated a tremendous volume of research.This dissertation targets the use of GPUs to enhance the performance of the solution of sparse linear systems using iterative methods complemented with state-of-the-art preconditioned techniques. In particular, we study ILUPACK, a package for the solution of sparse linear systems via Krylov subspace methods that relies on a modern inverse-based multilevel ILU (incomplete LU) preconditioning technique.We present new data-parallel versions of the preconditioner and the most important solvers contained in the package that significantly improve its performance without affecting its accuracy. Additionally we enhance existing task-parallel versions of ILUPACK for shared- and distributed-memory systems with the inclusion of GPU acceleration. The results obtained show a sensible reduction in the runtime of the methods, as well as the possibility of addressing large-scale problems efficiently.

scholarly journals A two-qubit photonic quantum processor and its application to solving systems of linear equations

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Stefanie Barz ◽  
Ivan Kassal ◽  
Martin Ringbauer ◽  
Yannick Ole Lipp ◽  
Borivoje Dakić ◽  
...  
Keyword(s):  
Large Scale ◽  
Linear Equations ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Single Qubit ◽  
Quantum Processor ◽  
Systems Of Linear Equations ◽  
Significant Obstacle

Abstract Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations.

New Algorithms for Secure Outsourcing of Large-Scale Systems of Linear Equations

2015 ◽  
Vol 10 (1) ◽  
pp. 69-78 ◽  
Author(s):  
Xiaofeng Chen ◽  
Xinyi Huang ◽  
Jin Li ◽  
Jianfeng Ma ◽  
Wenjing Lou ◽  
...  
Keyword(s):  
Large Scale ◽  
Linear Equations ◽  
Large Scale Systems ◽  
Secure Outsourcing ◽  
Systems Of Linear Equations ◽  
New Algorithms
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