Multiplicative Quadrature via Logarithmic Means (MQLM) From Log-Linear Interpolation to High-Order Numerical Integration
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| Sprache: | Englisch |
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2026
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| _version_ | 1866901080395218944 |
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| author | Sousa Oliveira, Francisco Anderson de |
| author_facet | Sousa Oliveira, Francisco Anderson de |
| contents | <p><strong>Under Study</strong><br><br>This deposit contains the PDF version of the article “Multiplicative Quadrature via Logarithmic Means (MQLM): From Log-Linear Interpolation to High-Order Numerical Integration”.</p> <p>The work develops a multiplicative quadrature framework for positive integrands based on logarithmic means and log-linear interpolation. Its central idea is that, for suitable classes of positive functions, the relevant object to interpolate is not the function itself, but its logarithm. This leads to a numerical integration scheme adapted to the intrinsic multiplicative geometry of the problem.</p> <p>Within this framework, the article studies exactness on exponential-type families, consistency with log-linear structure, and the numerical behavior of the resulting quadrature rules in comparison with standard additive schemes. The perspective connects numerical integration, interpolation theory, and multiplicative functional structure in a unified formulation.</p> <p>Main mathematical themes:<br>- numerical integration;<br>- logarithmic means;<br>- log-linear interpolation;<br>- multiplicative quadrature;<br>- positive integrands;<br>- structure-adapted numerical methods.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19289974 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Multiplicative Quadrature via Logarithmic Means (MQLM) From Log-Linear Interpolation to High-Order Numerical Integration Sousa Oliveira, Francisco Anderson de numerical integration, logarithmic means, log-linear interpolation, multiplicative quadrature, positive integrands, structure-adapted numerical methods <p><strong>Under Study</strong><br><br>This deposit contains the PDF version of the article “Multiplicative Quadrature via Logarithmic Means (MQLM): From Log-Linear Interpolation to High-Order Numerical Integration”.</p> <p>The work develops a multiplicative quadrature framework for positive integrands based on logarithmic means and log-linear interpolation. Its central idea is that, for suitable classes of positive functions, the relevant object to interpolate is not the function itself, but its logarithm. This leads to a numerical integration scheme adapted to the intrinsic multiplicative geometry of the problem.</p> <p>Within this framework, the article studies exactness on exponential-type families, consistency with log-linear structure, and the numerical behavior of the resulting quadrature rules in comparison with standard additive schemes. The perspective connects numerical integration, interpolation theory, and multiplicative functional structure in a unified formulation.</p> <p>Main mathematical themes:<br>- numerical integration;<br>- logarithmic means;<br>- log-linear interpolation;<br>- multiplicative quadrature;<br>- positive integrands;<br>- structure-adapted numerical methods.</p> |
| title | Multiplicative Quadrature via Logarithmic Means (MQLM) From Log-Linear Interpolation to High-Order Numerical Integration |
| topic | numerical integration, logarithmic means, log-linear interpolation, multiplicative quadrature, positive integrands, structure-adapted numerical methods |
| url | https://doi.org/10.5281/zenodo.19289974 |