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Petković, Ivan 1977
Analiza procesnih i računskih iteracija primenom savremenih računarskih aritmetika
AutorstvoNekomercijalnoBez prerade 3.0 Srbija (CC BYNCND 3.0)
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Academic metadata
Doktorska disertacija
Prirodnomatematičke nauke

Univerzitet u Nišu
Elektronski fakultet
Katedra za matematiku
Other Theses Metadata
Analysis of processing and computing iterations applying advanced computer arithmetic
[I. Petković]
XII, 173 str.
Datum odbrane: 02.02.2012.
Stanković, Milena (mentor)
Budimac, Zoran (član komisije)
Janković, Dragan (član komisije)
Milentijević, Ivan (član komisije)
Stojković, Suzana (član komisije)
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 multipleprecision arithmetic and interval
arithmetic involved in the new standard IEEE 754 in 2008. Advance computer arithmetic,
first of all interval arithmetic and multiprecision 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 multiprecision 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
rootfinding algorithms of different structure, especially in a regime of variable
(dynamic) precision of applied multiprecision arithmetic.
Računarska aritmetika, Iteracije
519.6(043.3)
Serbian
533491862
Elektronska teza
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 multipleprecision arithmetic and interval
arithmetic involved in the new standard IEEE 754 in 2008. Advance computer arithmetic,
first of all interval arithmetic and multiprecision 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 multiprecision 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
rootfinding algorithms of different structure, especially in a regime of variable
(dynamic) precision of applied multiprecision arithmetic.