This deposit contains the PDF version of the article “Multiplicative Quadrature via Logarithmic Means (MQLM): From Log-Linear Interpolation to High-Order Numerical Integration”. 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. 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. Main mathematical themes:- numerical integration;- logarithmic means;- log-linear interpolation;- multiplicative quadrature;- positive integrands;- structure-adapted numerical methods.
Francisco Anderson de Sousa Oliveira (Sat,) studied this question.