Open AccessRegularised discretisations obtained from first‐kind Fredholm operator equations
Author(s) -
Fikioris George
Publication year - 2021
Publication title -
iet microwaves, antennas and propagation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.555
H-Index - 69
eISSN - 1751-8733
pISSN - 1751-8725
DOI - 10.1049/mia2.12047
Subject(s) - fredholm operator , equivalence (formal languages) , mathematics , fredholm integral equation , operator (biology) , fredholm theory , context (archaeology) , matrix (chemical analysis) , mathematical analysis , integral equation , pure mathematics , compact operator , computer science , materials science , biochemistry , chemistry , paleontology , repressor , composite material , biology , transcription factor , extension (predicate logic) , gene , programming language
Judicious discretisations of certain first‐kind Fredholm operator equations are tantamount to Fredholm infinite‐matrix equations of the second kind. We give detailed explanations for the occurrence of this interesting and useful phenomenon and carefully examine the behaviour of the discretisations, especially with respect to matrix condition numbers. Our main tool is a certain equivalence of the discretisations――within the context of finite matrices―to discretisations of Fredholm operator equations of the second kind.