Title
Analiza procesnih i računskih iteracija primenom savremenih računarskih aritmetika
Creator
Petković, Ivan 1977-
Copyright date
2011
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
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Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 02.02.2012.
Other responsibilities
mentor
Stanković, Milena
član komisije
Budimac, Zoran
član komisije
Janković, Dragan
član komisije
Milentijević, Ivan
član komisije
Stojković, Suzana
Academic Expertise
Prirodno-matematičke nauke
Academic Title
-
University
Univerzitet u Nišu
Faculty
Elektronski fakultet
Group
Katedra za matematiku
Alternative title
Analysis of processing and computing iterations applying advanced computer arithmetic
Publisher
[I. Petković]
Format
XII, 173 str.
Abstract (en)
The proposed theme relates to the field of application of modern computer arithmetics
in the analysis of process performance and computational iterations, where the concept of
the modern computer arithmetic applies to multiple-precision arithmetic and interval
arithmetic involved in the new standard IEEE 754 in 2008. Advance computer arithmetic,
first of all interval arithmetic and multi-precision arithmetic, are employed in the the
dissertation for the analysis of matrix models in the design iteration process software and
iterative numerical computations. These are important and current research topics from
the point at which the application is working in the world. Research in this area have led
to the development and analysis of algorithms to control the accuracy, optimality, rate
calculations and other performance aspects of various processes such as designing
software and hardware, designing industrial products, transportation optimization,
modeling systems, the implementation of numerical algorithms and others.
The first part of dissertation is devoted to engineering design and development of new
products, which are either industrial products, technical innovations, hardware or
software, often contain a very complex set of relationships among many coupled tasks.
Controlling, redesigning and identifying features of these tasks can be usefully performed
by a suitable model based on the design structure matrix in an iteration procedure. The
proposed interval matrix model of design iteration controls and predicts slow and rapid
convergence of iteration work on tasks within a project. A new model is based on Perron-
Frobenius theorem and interval linear algebra where intervals and interval matrices are
employed instead of real numbers and real matrices. In this way a more relaxed
quantitative estimation of tasks is achieved and the presence of undetermined quantities is
allowed to a certain extent. The presented model is demonstrated in the example of
simplified software development process. An additional contribution in this dissertation
is the ranking of tasks within a design mode using components of eigenvalue vector
corresponding to the spectral radius of design structure matrix.
The second part deals with computational efficiency of numerical iterative algorithms.
Computational cost of iterative procedures for the implementation of basic arithmetic
operations in multi-precision arithmetic are studied and later applied for the analysis of
computational efficiency of the iterative methods for solving nonlinear equations. A new
approach that deals with the weights of employed arithmetic operations, involved in the
realization of these algorithms, is proposed. This enables a precise ranking of considered
root-finding algorithms of different structure, especially in a regime of variable
(dynamic) precision of applied multi-precision arithmetic.
Authors Key words
Računarska aritmetika, Iteracije
Classification
519.6(043.3)
Type
Elektronska teza
Abstract (en)
The proposed theme relates to the field of application of modern computer arithmetics
in the analysis of process performance and computational iterations, where the concept of
the modern computer arithmetic applies to multiple-precision arithmetic and interval
arithmetic involved in the new standard IEEE 754 in 2008. Advance computer arithmetic,
first of all interval arithmetic and multi-precision arithmetic, are employed in the the
dissertation for the analysis of matrix models in the design iteration process software and
iterative numerical computations. These are important and current research topics from
the point at which the application is working in the world. Research in this area have led
to the development and analysis of algorithms to control the accuracy, optimality, rate
calculations and other performance aspects of various processes such as designing
software and hardware, designing industrial products, transportation optimization,
modeling systems, the implementation of numerical algorithms and others.
The first part of dissertation is devoted to engineering design and development of new
products, which are either industrial products, technical innovations, hardware or
software, often contain a very complex set of relationships among many coupled tasks.
Controlling, redesigning and identifying features of these tasks can be usefully performed
by a suitable model based on the design structure matrix in an iteration procedure. The
proposed interval matrix model of design iteration controls and predicts slow and rapid
convergence of iteration work on tasks within a project. A new model is based on Perron-
Frobenius theorem and interval linear algebra where intervals and interval matrices are
employed instead of real numbers and real matrices. In this way a more relaxed
quantitative estimation of tasks is achieved and the presence of undetermined quantities is
allowed to a certain extent. The presented model is demonstrated in the example of
simplified software development process. An additional contribution in this dissertation
is the ranking of tasks within a design mode using components of eigenvalue vector
corresponding to the spectral radius of design structure matrix.
The second part deals with computational efficiency of numerical iterative algorithms.
Computational cost of iterative procedures for the implementation of basic arithmetic
operations in multi-precision arithmetic are studied and later applied for the analysis of
computational efficiency of the iterative methods for solving nonlinear equations. A new
approach that deals with the weights of employed arithmetic operations, involved in the
realization of these algorithms, is proposed. This enables a precise ranking of considered
root-finding algorithms of different structure, especially in a regime of variable
(dynamic) precision of applied multi-precision arithmetic.
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