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Recursive families of higher order iterative maps

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Mário M. Graça

Numerical Analysis · Submitted 18 May 2014

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

The authors' main claim To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence.

how it is stated · asserted 0.99 read the record →

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arXiv ID1405.4492 (version 1)
Pith IDXGBONWPY, Pith's permanent record of this paper and its review
CitationM\'ario M. Gra\c{c}a. "Recursive families of higher order iterative maps." arXiv:1405.4492 (2014). https://pith.science/paper/XGBONWPY
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The compiled record

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,523 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence. These maps are based on model functions which can be written as an inner product. The main family of maps discussed is defined recursively and is called {\it Newton-barycentric}. We illustrate the application of Newton-barycentric maps in two worked examples, one dealing with a typical least squares problem and the other showing how to locate simultaneously a great number of extrema of the Ackley's function.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence. contribution 0.77 0.85 0.19 asserted 0.99
s1 These maps are based on model functions which can be written as an inner product. method 0.98 0.65 0.05 asserted 1.00
s2 The main family of maps discussed is defined recursively and is called {\it Newton-barycentric}. contribution 0.67 0.86 0.19 asserted 1.00
s3 We illustrate the application of Newton-barycentric maps in two worked examples, one dealing with a typical least squares problem and the other showing how to locate simultaneously a great number of extrema of the Ackley's function. contribution 0.65 0.92 0.14 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.62.

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sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence. These maps are based on model functions which can be written as an inner product. The main family of maps discussed is defined recursively and is called {\it Newton-barycentric}. We illustrate the application of Newton-barycentric maps in two worked examples, one dealing with a typical least squares problem and the other showing how to locate simultaneously a great number of extrema of the Ackley's function.

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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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