A Step Forward to Formalize Tailored to Problem Specificity Mathematical Transforms

Antonio Glaría, Rodrigo Salas, Stéren Chabert, Pablo Roncagliolo, Alexis Arriola, Gonzalo Tapia, Matías Salinas, Herman Zepeda, Carla Taramasco, Kayode Oshinubi, Jacques Demongeot

Research output: Contribution to journalArticlepeer-review


Linear functional analysis historically founded by Fourier and Legendre played a significant role to provide a unified vision of mathematical transformations between vector spaces. The possibility of extending this approach is explored when basis of vector spaces is built Tailored to the Problem Specificity (TPS) and not from the convenience or effectiveness of mathematical calculations. Standardized mathematical transformations, such as Fourier or polynomial transforms, could be extended toward TPS methods, on a basis, which properly encodes specific knowledge about a problem. Transition between methods is illustrated by comparing what happens in conventional Fourier transform with what happened during the development of Jewett Transform, reported in previous articles. The proper use of computational intelligence tools to perform Jewett Transform allowed complexity algorithm optimization, which encourages the search for a general TPS methodology.

Original languageEnglish
Article number855862
JournalFrontiers in Applied Mathematics and Statistics
Publication statusPublished - 20 Jun 2022


  • Dynalet transform
  • ELM
  • mathematical transforms
  • model-based data processing
  • non-orthogonal basis

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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