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On the lack of monotonicity of Newton-Hewer updates for Riccati equations

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Mohammad Akbari, Bahman Gharesifard, Tamas Linder

Optimization and Control · Submitted 29 Oct 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We provide a set of counterexamples for the monotonicity of the Newton-Hewer method for solving the discrete-time algebraic Riccati equation in dynamic settings, drawing a contrast with the Riccati difference equation.

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arXiv ID2010.15983 (version 1)
Pith IDRGNQPTX2, Pith's permanent record of this paper and its review
CitationBahman Gharesifard, Mohammad Akbari, Tamas Linder. "On the lack of monotonicity of Newton-Hewer updates for Riccati equations." arXiv:2010.15983 (2020). https://pith.science/paper/RGNQPTX2
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,661 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.28 · human participants 0.02 · controlled comparison 0.18 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.91 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We provide a set of counterexamples for the monotonicity of the Newton-Hewer method for solving the discrete-time algebraic Riccati equation in dynamic settings, drawing a contrast with the Riccati difference equation.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We provide a set of counterexamples for the monotonicity of the Newton-Hewer method for solving the discrete-time algebraic Riccati equation in dynamic settings, drawing a contrast with the Riccati difference equation. contribution 0.91 0.93 0.89 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.64.

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Original abstract

We provide a set of counterexamples for the monotonicity of the Newton-Hewer method for solving the discrete-time algebraic Riccati equation in dynamic settings, drawing a contrast with the Riccati difference equation.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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  • One of the main reason for the difficulty of establishing this result is the lack of monotonicity of the evolutions of the Newton-Hewer dynamics with respect to the underlying system parameter, a sharp contrast with the Riccati difference updates [ref] , which we have recently reported in [ref] .

    An Iterative Riccati Algorithm for Online Linear Quadratic Control · Strong Stability · 0.93

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