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- W4321451954 abstract "In a paper from 1986, Păvăloiu cite{Pavaloiu 1986} has considered the fixed point problem (in Banach space setting)[x=lambda Dleft( xright) +y, qquad lambdain {mathbb R},]written in the form (x -lambda Dleft( xright) -y) and solved by the quasi-Newton iterates[x_{n+1}=x_{n}-Aleft( x_{n}right) left[ x_{n}-lambda Dleft(x_{n}right) -yright] ,qquad n=0,1,ldots]Semilocal convergence results were obtained, ensuring linear convergence of these iterates as well as for those resulting from a special instance of (A(x),) when given by a certain approximation of the inverse of the Jacobian of (x-lambda Dleft( xright) -y:)[x_{n+1}=x_{n}-[1+lambda D^primeleft( x_{n}right)] left[x_{n}+lambda Dleft( x_{n}right) -yright] ,qquad n=0,1,ldots]In this note, we analyze the local convergence of those iterates, and, using the Ostrowski local attraction theorem, we give some sufficient conditions such that the iterates converge locally both linearly and with higher convergence orders." @default.
- W4321451954 created "2023-02-22" @default.
- W4321451954 creator A5063526386 @default.
- W4321451954 date "2015-12-18" @default.
- W4321451954 modified "2023-10-17" @default.
- W4321451954 title "On the convergence of some quasi-Newton iterates studied by I. Păvăloiu" @default.
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- W4321451954 doi "https://doi.org/10.33993/jnaat441-1069" @default.
- W4321451954 hasPublicationYear "2015" @default.
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