FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2151567102> ?p ?o ?g. }

• W2151567102 abstract "The area of approximate algebraic computations is a fast growing area in modern computer algebra which has attracted many researchers in recent years. Amongst the various algebraic computations, the computation of the Greatest Common Divisor (GCD) and the Least Common Multiple (LCM) of a set of polynomials are challenging problems that arise from several applications in applied mathematics and engineering. Several methods have been proposed for the computation of the GCD of polynomials using tools and notions either from linear algebra or linear systems theory. Amongst these, a matrix-based method which relies on the properties of the GCD as an invariant of the original set of polynomials under elementary row transformations and shifting elements in the rows of a matrix, shows interesting properties in relation to the problem of the GCD of sets of many polynomials. These transformations are referred to as Extended-Row-Equivalence and Shifting (ERES) operations and their iterative application to a basis matrix, which is formed directly from the coefficients of the given polynomials, formulates the ERES method for the computation of the GCD of polynomials and establishes the basic principles of the ERES methodology. The main objective of the present thesis concerns the improvement of the ERES methodology and its use for the efficient computation of the GCD and LCM of sets of several univariate polynomials with parameter uncertainty, as well as the extension of its application to other related algebraic problems. New theoretical and numerical properties of the ERES method are defined in this thesis by introducing the matrix representation of the Shifting operation, which is used to change the position of the elements in the rows of a matrix. This important theoretical result opens the way for a new algebraic representation of the GCD of a set polynomials, the remainder, and the quotient of Euclid's division for two polynomials based on ERES operations. The principles of the ERES methodology provide the means to develop numerical algorithms for the GCD and LCM of polynomials that inherently have the potential to efficiently work with sets of several polynomials with inexactly known coefficients. The present new implementation of the ERES method, referred to as the ``Hybrid ERES Algorithm, is based on the effective combination of symbolic-numeric arithmetic (hybrid arithmetic) and shows interesting computational properties concerning the approximate GCD and LCM problems. The evaluation of the quality, or ``strength, of an approximate GCD is equivalent to an evaluation of a distance problem in a projective space and it is thus reduced to an optimisation problem. An efficient implementation of an algorithm computing the strength bounds is introduced here by exploiting some of the special aspects of the respective distance problem. Furthermore, a new ERES-based method has been developed for the approximate LCM which involves a least-squares minimisation process, applied to a matrix which is formed from the remainders of Euclid's division by ERES operations. The residual from the least-squares process characterises the quality of the obtained approximate LCM. Finally, the developed framework of the ERES methodology is also applied to the representation of continued fractions to improve the stability criterion for linear systems based on the Routh-Hurwitz test." @default.
• W2151567102 created "2016-06-24" @default.
• W2151567102 creator A5039933390 @default.
• W2151567102 date "2011-10-01" @default.
• W2151567102 modified "2023-09-24" @default.
• W2151567102 title "ERES Methodology and Approximate Algebraic Computations" @default.
• W2151567102 cites W130500341 @default.
• W2151567102 cites W1485446097 @default.
• W2151567102 cites W1556970733 @default.
• W2151567102 cites W1572189095 @default.
• W2151567102 cites W1598464121 @default.
• W2151567102 cites W1602290632 @default.
• W2151567102 cites W1965692635 @default.
• W2151567102 cites W1966287322 @default.
• W2151567102 cites W1966711586 @default.
• W2151567102 cites W1967281400 @default.
• W2151567102 cites W1967467218 @default.
• W2151567102 cites W1971119115 @default.
• W2151567102 cites W1976910007 @default.
• W2151567102 cites W1977106683 @default.
• W2151567102 cites W1977579021 @default.
• W2151567102 cites W1988442902 @default.
• W2151567102 cites W1989356517 @default.
• W2151567102 cites W1990436029 @default.
• W2151567102 cites W1996842728 @default.
• W2151567102 cites W2005423095 @default.
• W2151567102 cites W2007191224 @default.
• W2151567102 cites W2017333591 @default.
• W2151567102 cites W2018572153 @default.
• W2151567102 cites W2020156690 @default.
• W2151567102 cites W2024918578 @default.
• W2151567102 cites W2036474546 @default.
• W2151567102 cites W2059557631 @default.
• W2151567102 cites W2061311874 @default.
• W2151567102 cites W2066692963 @default.
• W2151567102 cites W2070448713 @default.
• W2151567102 cites W2074156531 @default.
• W2151567102 cites W2074424999 @default.
• W2151567102 cites W2075665712 @default.
• W2151567102 cites W2077315987 @default.
• W2151567102 cites W2078643711 @default.
• W2151567102 cites W2080892223 @default.
• W2151567102 cites W2085849252 @default.
• W2151567102 cites W2088028877 @default.
• W2151567102 cites W2093406485 @default.
• W2151567102 cites W2093972952 @default.
• W2151567102 cites W2094533795 @default.
• W2151567102 cites W2109445883 @default.
• W2151567102 cites W2116318259 @default.
• W2151567102 cites W2117026915 @default.
• W2151567102 cites W2117461673 @default.
• W2151567102 cites W2120672240 @default.
• W2151567102 cites W2121836583 @default.
• W2151567102 cites W2130331374 @default.
• W2151567102 cites W2131705730 @default.
• W2151567102 cites W2133176805 @default.
• W2151567102 cites W2137879196 @default.
• W2151567102 cites W2140382237 @default.
• W2151567102 cites W2140710461 @default.
• W2151567102 cites W2142335183 @default.
• W2151567102 cites W2147831117 @default.
• W2151567102 cites W2150200785 @default.
• W2151567102 cites W2157995467 @default.
• W2151567102 cites W2163578008 @default.
• W2151567102 cites W2266890262 @default.
• W2151567102 cites W2279195201 @default.
• W2151567102 cites W2288288427 @default.
• W2151567102 cites W2329233948 @default.
• W2151567102 cites W2562393118 @default.
• W2151567102 cites W2613784664 @default.
• W2151567102 cites W2798813531 @default.
• W2151567102 cites W2798909945 @default.
• W2151567102 cites W3104794861 @default.
• W2151567102 cites W3126588943 @default.
• W2151567102 cites W349985708 @default.
• W2151567102 cites W594073344 @default.
• W2151567102 cites W59802204 @default.
• W2151567102 cites W864649105 @default.
• W2151567102 cites W96267676 @default.
• W2151567102 hasPublicationYear "2011" @default.
• W2151567102 type Work @default.
• W2151567102 sameAs 2151567102 @default.
• W2151567102 citedByCount "0" @default.
• W2151567102 crossrefType "dissertation" @default.
• W2151567102 hasAuthorship W2151567102A5039933390 @default.
• W2151567102 hasConcept C102607178 @default.
• W2151567102 hasConcept C106487976 @default.
• W2151567102 hasConcept C110812573 @default.
• W2151567102 hasConcept C11413529 @default.
• W2151567102 hasConcept C118615104 @default.
• W2151567102 hasConcept C125257309 @default.
• W2151567102 hasConcept C134306372 @default.
• W2151567102 hasConcept C136119220 @default.
• W2151567102 hasConcept C139352143 @default.
• W2151567102 hasConcept C159985019 @default.
• W2151567102 hasConcept C163834973 @default.
• W2151567102 hasConcept C190470478 @default.
• W2151567102 hasConcept C192562407 @default.
• W2151567102 hasConcept C202444582 @default.
• W2151567102 hasConcept C2524010 @default.

• next