Applications of a Numerical Spectral Expansion Method to Problems in Physics; a Retrospective

2010 ◽  
pp. 409-426 ◽  
Author(s):  
George H. Rawitscher
Keyword(s):  
Expansion Method ◽  
Spectral Expansion

Linear inversion of gravity data using the spectral expansion method

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 820-824 ◽  
Author(s):  
Rene E. Chavez ◽  
George D. Garland
Keyword(s):  
Inverse Problem ◽  
Gravity Data ◽  
Linear Equations ◽  
Thin Sheet ◽  
Gravity Anomalies ◽  
Expansion Method ◽  
Spectral Expansion ◽  
Uniform Density ◽  
Linear Inversion ◽  
Prismatic Structure

Inversion of gravity anomalies in terms of an anomalous mass distribution with irregular outline but uniform density leads to a nonlinear inverse problem. An alternative approach based on the thin‐sheet approximation can, however, be formulated as a linear inverse problem provided the structures are two‐dimensional. The anomalous mass is represented by a thin sheet, which is located at a depth [Formula: see text] and is divided into M strips with N < M data points. Thus, an underdetermined system of linear equations is obtained which is solved by the spectral expansion method for the surface density distribution of each segment. This set of parameters is then transformed into a prismatic structure with variable depth but uniform density. The modeling procedure involves a noniterative method. A gravity problem is investigated, and the solution obtained compares well with previous interpretations.

scholarly journals Spectral expansion method for analysis of a system with shifted Erlang and hyper-Erlang distributions

2021 ◽  
Vol 24 (2) ◽  
pp. 55-61
Author(s):  
Veniamin N. Tarasov ◽  
Nadezhda F. Bakhareva
Keyword(s):  
Waiting Time ◽  
Queuing Theory ◽  
Expansion Method ◽  
Spectral Expansion ◽  
Queuing System ◽  
Erlang Distribution ◽  
Modern Theory ◽  
Calculation Formula ◽  
Average Waiting Time ◽  
Erlang Distributions

In this paper, we obtained a spectral expansion of the solution to the Lindley integral equation for a queuing system with a shifted Erlang input flow of customers and a hyper-Erlang distribution of the service time. On its basis, a calculation formula is derived for the average waiting time in the queue for this system in a closed form. As you know, all other characteristics of the queuing system are derivatives of the average waiting time. The resulting calculation formula complements and expands the well-known unfinished formula for the average waiting time in queue in queuing theory for G/G/1 systems. In the theory of queuing, studies of private systems of the G/G/1 type are relevant due to the fact that they are actively used in the modern theory of teletraffic, as well as in the design and modeling of various data transmission systems.

Tipp and the Spectral Expansion Method

1995 ◽  
pp. 99-113 ◽  
Author(s):  
I. Mitrani ◽  
A. Ost ◽  
M. Rettelbach
Keyword(s):  
Expansion Method ◽  
Spectral Expansion

scholarly journals Spectral Expansion Method for Cloud Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
K. Kotteswari ◽  
A. Bharathi
Keyword(s):  
Data Storage ◽  
Service Providers ◽  
Expansion Method ◽  
Cloud Service ◽  
Spectral Expansion ◽  
Performance Model ◽  
Hybrid Network ◽  
Performance Modelling ◽  
Technology Application ◽  
Cloud Service Providers

Cloud computing is a computing hypothesis, where a huge group of systems is linked together in private, public, or hybrid network, to offer dynamically amendable infrastructure for data storage, file storage, and application. With this emerging technology, application hosting, delivery, content storage, and reduced computation cost are achieved, and it acts as an essential module for the backbone of the Internet of Things (IoT). The efficiency of cloud service providers (CSP) could be improved by considering significant factors such as availability, reliability, usability, security, responsiveness, and elasticity. Assessment of these factors leads to efficiency in designing a scheduler for CSP. These metrics also improved the quality of service (QoS) in the cloud. Many existing models and approaches evaluate these metrics. But these existing approaches do not offer efficient outcome. In this paper, a prominent performance model named the “spectral expansion method (SPM)” evaluates cloud reliability. The spectral expansion method (SPM) is a huge technique useful in reliability and performance modelling of the computing system. This approach solves the Markov model of cloud service providers (CSP) to predict the reliability. The SPM is better compared to matrix-geometric methods.

scholarly journals Analytical Modelling and Performability Evaluation of Multi-Channel WLANs with Global Failures

2015 ◽  
Vol 10 (4) ◽  
pp. 551 ◽  
Author(s):  
Yoney Kirsal-Ever ◽  
Yonal Kirsal ◽  
Enver Ever ◽  
Orhan Gemikonakli
Keyword(s):  
Ieee 802.11 ◽  
Local Area Network ◽  
Blocking Probability ◽  
Expansion Method ◽  
Local Area ◽  
Spectral Expansion ◽  
Analytical Modelling ◽  
Area Network ◽  
Critical Function ◽  
Function Unit

<pre>Wireless local area networks (<span>WLANs</span>) which are based on IEEE 802.11 standard are used widely in existing local area network configurations. IEEE 802.11 offers multiple non-overlapping channels to increase the capacity of the network. There are strong evidences that <span>WLANs</span> are prone to impairments. In order to improve the quality of service (QoS) and to evaluate the performance of <span>WLANs</span> realistically, the availability of the systems should be considered. This paper studies <span>performability</span> evaluation of a multi-channel <span>WLAN</span> using analytical modelling approach. Unlike the existing studies, the failures of the overall system, where a critical function unit fails making all the channels unavailable are considered. A new term is introduced as global failures. It is possible to solve the models considered using matrix geometric method where system parameters and minimal non negative solution <span>R</span> is computed by an iterative method. However spectral expansion method is a well-known alternative where the iterative calculations for solving <span>R</span> is avoided using eigenvalues and eigenvectors. The exact spectral expansion method is employed to obtain <span>performability</span> measures such as mean queue length and blocking probability. Iterative refinements are employed in solution of simultaneous equations.</pre>

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