Geodesic
Root-multiplicity and root iterative refinement
Filomat, Tome 37 (2023) no. 26, p. 8995

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DOI

We discuss root-finding algorithms for multiple zeros of nonlinear equations in one variable. Re- cent investigations regarding this problem were mainly aimed at deriving schemes that use the beforehand knowledge of root multiplicity. In this communication we investigate several such root-finding methods under the assumption that the multiplicity of the sought root is not early known. We analyze strategies where root refinement is calculated along side to its multiplicity assessment, and put them to use through numerical experiments. Presented results go in favor of a more realistic use of the analysed methods.
DOI : 10.2298/FIL2326995D
Classification : 65H05
Keywords: Nonlinear equations, Multiple roots, Multipoint methods, Convergence order 
Jovana Džunić. Root-multiplicity and root iterative refinement. Filomat, Tome 37 (2023) no. 26, p. 8995 . doi: 10.2298/FIL2326995D
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     author = {Jovana D\v{z}uni\'c},
     title = {Root-multiplicity and root iterative refinement},
     journal = {Filomat},
     pages = {8995 },
     year = {2023},
     volume = {37},
     number = {26},
     doi = {10.2298/FIL2326995D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2326995D/}
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