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More precisely, we assume that only the averages of\n                    <jats:italic>f<\/jats:italic>\n                    over a given triangulation\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\mathcal {T}_N$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>T<\/mml:mi>\n                            <mml:mi>N<\/mml:mi>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varOmega $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mi>\u03a9<\/mml:mi>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    are available and seek a bivariate polynomial that approximates\n                    <jats:italic>f<\/jats:italic>\n                    using a histopolation approach, potentially flanked by an additional regression technique. This methodology relies on the selection of a subset of triangles\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\mathcal {T}_M \\subset \\mathcal {T}_N$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>T<\/mml:mi>\n                              <mml:mi>M<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo>\u2282<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>T<\/mml:mi>\n                              <mml:mi>N<\/mml:mi>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    for histopolation, ensuring both the solvability and the well-conditioning of the problem. The remaining triangles can potentially be used to enhance the accuracy of the polynomial approximation through a simultaneous regression. We will introduce histopolation and combined histopolation-regression methods using the Padua points, discrete Leja sequences, and approximate Fekete nodes. The proposed algorithms are implemented and evaluated through numerical experiments that demonstrate their effectiveness in function approximation.\n                  <\/jats:p>","DOI":"10.1007\/s10444-026-10309-4","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:48:17Z","timestamp":1777902497000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bivariate polynomial histopolation techniques on Padua, Fekete, and Leja triangles"],"prefix":"10.1007","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5246-8049","authenticated-orcid":false,"given":"Ludovico","family":"Bruni\u00a0Bruno","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Dell\u2019Accio","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wolfgang","family":"Erb","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Federico","family":"Nudo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"key":"10309_CR1","doi-asserted-by":"publisher","first-page":"109964","DOI":"10.1016\/j.jcp.2020.109964","volume":"428","author":"A Alonso Rodr\u00edguez","year":"2021","unstructured":"Alonso Rodr\u00edguez, A., Rapetti, F.: On a generalization of the Lebesgue\u2019s constant. 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