Error bounds for Newton's iterates derived from the Kantorovich theorem

DOI10.1007/BF01389444zbMath0567.65027OpenAlexW2071095292MaRDI QIDQ1059985

Tetsuro Yamamoto

Publication date: 1986

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133060

zbMATH Keywords

error boundsupper and lower boundsKantorovich theoremGragg-Tapia's techniqueKantorovich recurrence relationsMiel's boundsNewton iteratesPotra-Ptak's bounds

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

A convergence theorem for Newton-like methods in Banach spaces ⋮ Asymptotics in the Thurstone model with an increasing items ⋮ Error bounds for Newton-like methods under Kantorovich type assumptions, II ⋮ On the semilocal convergence behavior for Halley's method ⋮ The Kantorovich theorem and interior point methods ⋮ A convergence theorem for Newton’s method in Banach spaces ⋮ Historical developments in convergence analysis for Newton's and Newton-like methods ⋮ The theory of Newton's method ⋮ Interval mathematics, algebraic equations and optimization ⋮ A unified derivation of several error bounds for Newton's process

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