Average-Case Optimality of a Hybrid Secant-Bisection Method

DOI10.2307/2153369zbMath0849.65029OpenAlexW2025645456MaRDI QIDQ4878510

Klaus Ritter, Erich Novak, Henryk Woźniakowski

Publication date: 11 November 1996

Full work available at URL: https://doi.org/10.2307/2153369

zbMATH Keywords

stopping ruleaverage-case complexityzerofindingaverage-case optimalityhybrid Newton-bisection methodhybrid secant-bisection method

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Complexity and performance of numerical algorithms (65Y20)

Related Items (9)

Lower bound on complexity of optimization of continuous functions ⋮ Unnamed Item ⋮ ON NEW HYBRID ROOT-FINDING ALGORITHMS FOR SOLVING TRANSCENDENTAL EQUATIONS USING EXPONENTIAL AND HALLEY'S METHODS ⋮ A new trigonometrical algorithm for computing real root of non-linear transcendental equations ⋮ A note on two fixed point problems ⋮ Adaptive approximation of the minimum of Brownian motion ⋮ A lower bound on complexity of optimization under the \(r\)-fold integrated Wiener measure ⋮ A method to accelerate the convergence of the secant algorithm ⋮ Why does information-based complexity use the real number model?

Uses Software

• UNCMND
• pchip
• zeroin

Cites Work

• Optimal solution of nonlinear equations
• Average errors for zero finding: Lower bounds for smooth or monotone functions
• Information of varying cardinality
• Some complexity results for zero finding for univariate functions
• Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function
• On Enclosing Simple Roots of Nonlinear Equations
• Designs for Regression Problems with Correlated Errors III
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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