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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id custom-type="elpub" pub-id-type="custom">najo-1031</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Relationship plurality approximation</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Lukyanov</surname><given-names>V. D.</given-names></name></name-alternatives><bio xml:lang="en"><p>Saint Petersburg</p></bio><email xlink:type="simple">lukyanovvd@rambler.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="en">JSC Avangard<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2014</year></pub-date><pub-date pub-type="epub"><day>15</day><month>08</month><year>2025</year></pub-date><volume>5</volume><issue>3</issue><fpage>384</fpage><lpage>390</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Lukyanov V.D., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Lukyanov V.D.</copyright-holder><copyright-holder xml:lang="en">Lukyanov V.D.</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/1031">https://nanojournal.ifmo.ru/jour/article/view/1031</self-uri><abstract><p>An algorithm for the approximation of relationship pluralities is set by linear combinations of functions with unknown coefficients, which in part coincides in all relationship pluralities having been built using ordinary least squares. Examples of the algorithm’s realization, when finding particular solutions plurality of linear nonhomogeneous differential equations, have been given.</p></abstract><kwd-group xml:lang="en"><kwd>approximation</kwd><kwd>ordinary least squares</kwd><kwd>dependences plurality</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Kobzar’ A.I. Applied Mathematical Statistics. For Engineers and Scientists. Moscow, Fizmatlit, 2006.</mixed-citation><mixed-citation xml:lang="en">Kobzar’ A.I. Applied Mathematical Statistics. For Engineers and Scientists. Moscow, Fizmatlit, 2006.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Seber G.A.F. Linear Regression Analysis. John Wiley and Sons. New York, London, Sydney, Toronto, 1977.</mixed-citation><mixed-citation xml:lang="en">Seber G.A.F. 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Nanosystems: Physics, Chemistry, Mathematics, 3 (6), P. 5–15 (2012).</mixed-citation><mixed-citation xml:lang="en">Lukyanov V.D. On the Issue of Interpolation Approximation Polynomial Construction. Nanosystems: Physics, Chemistry, Mathematics, 3 (6), P. 5–15 (2012).</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
