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Statements

Subject Item
n2:RIV%2F60461373%3A22340%2F14%3A43897765%21RIV15-MSM-22340___
rdf:type
n11:Vysledek skos:Concept
rdfs:seeAlso
http://etna.math.kent.edu/volumes/2011-2020/vol41/
dcterms:description
For finding the zeros of a coquaternionic polynomial p of degree n, the concept of a (real) companion polynomial q of degree 2n, is applied. If z0 is a root of q, then, based on z0, there is a simple formula for an element z with the property that (p(z))*p(z) = 0, thus z is a singular point of p. Under certain conditions, the same z has the property that p(z) = 0, thus z is a zero of p. There is an algorithm for finding zeros and singular points of p.. For finding zeros which are not similar to complex numbers, Newton's method is applied, and a simple technique for computing the exact Jacobi matrix is presented. For finding the zeros of a coquaternionic polynomial p of degree n, the concept of a (real) companion polynomial q of degree 2n, is applied. If z0 is a root of q, then, based on z0, there is a simple formula for an element z with the property that (p(z))*p(z) = 0, thus z is a singular point of p. Under certain conditions, the same z has the property that p(z) = 0, thus z is a zero of p. There is an algorithm for finding zeros and singular points of p.. For finding zeros which are not similar to complex numbers, Newton's method is applied, and a simple technique for computing the exact Jacobi matrix is presented.
dcterms:title
ZEROS AND SINGULAR POINTS FOR ONE-SIDED COQUATERNIONIC POLYNOMIALS WITH AN EXTENSION TO OTHER R4 ALGEBRAS ZEROS AND SINGULAR POINTS FOR ONE-SIDED COQUATERNIONIC POLYNOMIALS WITH AN EXTENSION TO OTHER R4 ALGEBRAS
skos:prefLabel
ZEROS AND SINGULAR POINTS FOR ONE-SIDED COQUATERNIONIC POLYNOMIALS WITH AN EXTENSION TO OTHER R4 ALGEBRAS ZEROS AND SINGULAR POINTS FOR ONE-SIDED COQUATERNIONIC POLYNOMIALS WITH AN EXTENSION TO OTHER R4 ALGEBRAS
skos:notation
RIV/60461373:22340/14:43897765!RIV15-MSM-22340___
n3:aktivita
n15:I
n3:aktivity
I
n3:cisloPeriodika
June
n3:dodaniDat
n4:2015
n3:domaciTvurceVysledku
n18:6810098
n3:druhVysledku
n10:J
n3:duvernostUdaju
n7:S
n3:entitaPredkladatele
n17:predkladatel
n3:idSjednocenehoVysledku
57316
n3:idVysledku
RIV/60461373:22340/14:43897765
n3:jazykVysledku
n16:eng
n3:klicovaSlova
Newton method; singular points for coquaternionic polynomials; companion polynomial for coquaternionic polynomials; zeros of coquaternionic polynomials
n3:klicoveSlovo
n6:Newton%20method n6:zeros%20of%20coquaternionic%20polynomials n6:singular%20points%20for%20coquaternionic%20polynomials n6:companion%20polynomial%20for%20coquaternionic%20polynomials
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[FF1D45506F8A]
n3:nazevZdroje
Electronic Transactions on Numerical Analysis
n3:obor
n13:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:rokUplatneniVysledku
n4:2014
n3:svazekPeriodika
Vol. 41
n3:tvurceVysledku
Janovská, Drahoslava Opfer, Gerhard
s:issn
1068-9613
s:numberOfPages
26
n8:organizacniJednotka
22340