Research

Journal Papers

• Bruni Bruno, L., De Marchi, S., Elefante, G., Polynomial approximation from diffused data: unisolvence and stability, BIT Numerical Mathematics 66 (2026)
  Multivariate histopolation on generic convex sets is explored. Unisolvence is related with algebraic varieties, and good distributions of supports are identified.
  DOI: https://doi.org/10.1007/s10543-026-01128-6

• Bruni Bruno, L., Dell'Accio, F., Erb, W., Nudo, F., Bivariate polynomial histopolation techniques on Padua, Fekete and Leja triangles, Advances in Computational Mathematics 52 (2026)
  An algorithm for the selection of good bivariate supports for histopolation is provided. Such supports are triangles related with Padua points.
  DOI: https://doi.org/10.1007/s10444-026-10309-4

• Bruni Bruno, L., Piazzon, F., The Lebesgue constant for uniform approximation of differential forms, Journal of Mathematical Analysis and Applications 562 (2026)
  A very large concept of Lebesgue constant for fitting of differential forms is given. The relationship of this quantity with the norm of the weights-based projector is studied.
  DOI: https://doi.org/10.1016/j.jmaa.2026.130687

• Bruni Bruno, L., Semplice, M., Serra-Capizzano, S., The numerical linear algebra of weights. Part 1: from the spectral analysis to conditioning and preconditioning in the one-dimensional Laplacian case, BIT Numerical Mathematics 65 (2025)
  The localization features of weights — geometrical degrees of freedom for Whitney forms — are exploited to analyze the spectral features of stiffness matrices arising in FEM.
  DOI: https://doi.org/10.1007/s10543-025-01088-3

• Bruni Bruno, L., Dell'Accio, F., Erb, W., Nudo, F., Polynomial histopolation on mock-Chebyshev segments, Journal of Scientific Computing 105 (2025)
  Histopolation on uniform segments leads to the Runge phenomenon. Lumping neighbouring segments yields Chebyshev-like convergence.
  DOI: https://doi.org/10.1007/s10915-025-02977-z

• Bruni Bruno, L., Erb, W., The Fekete problem in segmental polynomial interpolation, BIT Numerical Mathematics 65 (2025)
  The identification of efficient segments for histopolation is performed by maximizing the determinant of the Vandermonde matrix.
  DOI: https://doi.org/10.1007/s10543-024-01047-4

• Bruni Bruno, L., Erb, W., Polynomial interpolation of function averages on interval segments, SIAM Journal on Numerical Analysis 92 (2024)
  Existence and uniqueness for histopolation are established, and the relative Lebesgue constant is characterized. Estimates for relevant classes of segments and convergence results are given.
  DOI: https://doi.org/10.1137/23M1598271

• Alonso Rodríguez, A., Bruni Bruno, L., Rapetti, F., Whitney edge elements and the Runge phenomenon, Journal of Computational and Applied Mathematics 427 (2023)
  Whitney 1-forms may exhibit wild oscillations. This is proved to be a consequence of the nodal multivariate Runge phenomenon. This work was awarded the 2022 ESCO best student paper.
  DOI: https://doi.org/10.1016/j.cam.2023.115117

• Bruni Bruno, L., Zampa, E., Unisolvent and minimal degrees of freedom for the second family of polynomial differential forms, ESAIM: Mathematical Modeling and Numerical Analysis 56 (2022)
  Unisolvence results for complete polynomial differential forms are given in an algebraic-topological fashion: the selection of the middle spaces is avoided owing to the five lemma.
  DOI: https://doi.org/10.1051/m2an/2022088

• Alonso Rodríguez, A., Bruni Bruno, L., Rapetti, F., Towards nonuniform distributions of unisolvent weights for high-order Whitney edge elements, Calcolo 59 (2022)
  The Lebesgue constant for differential forms is estimated for the first time. Optimization techniques based on warping and blending techniques are proposed.
  DOI: https://doi.org/10.1007/s10092-022-00481-6

Proceedings and papers in special issues

• Bruni Bruno, L., Elefante, G., An algorithm for the estimation of the segmental Lebesgue constant, Journal of Computational and Applied Mathematics 471 (2026)
  Computing Lebesgue constants in histopolation is expensive. An efficient algorithm for the case of differential 1-forms is proposed and compared.
  DOI: https://doi.org/10.1016/j.cam.2025.116745

• Bruni Bruno, L., Piazzon, F., A pluripotential theoretic framework for polynomial interpolation of vector-valued functions and differential forms, Dolomites Research notes on Approximation 17 (2024)
  A theoretical formalization of Fekete currents for differential forms is given. This paper is dedicated to Len Bos in occasion of his retirement.
  DOI: https://doi.org/10.14658/PUPJ-DRNA-2024-3-12

• Alonso Rodríguez, A., Bruni Bruno, L., Rapetti, F., Flexible weights for high order face based finite element interpolation, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1, LNCSE 137 (2023)
  The specfic case of face interpolation by weights is studied on a tetrahedron. The corresponding degrees of freedom give conforming high order finite element spaces.
  DOI: https://doi.org/10.1007/978-3-031-20432-6_5

• Alonso Rodríguez, A., Bruni Bruno, L., Rapetti, F., Computing weights for high order Whitney edge elements, Dolomites research notes on approximation 15 (2022)
  Explicit formulae for the computation of weights are given. Such techniques reflect the coordinate-free representation of Whitney forms.
  DOI: https://doi.org/10.14658/PUPJ-DRNA-2022-2-1

• Alonso Rodríguez, A., Bruni Bruno, L., Rapetti, F., Minimal sets of unisolvent weights for high order Whitney forms on simplices, Numerical Mathematics and Advanced Applications ENUMATH 2019, LNCSE 139 (2020)
  Weights for high order Whitney forms are generally presented as a redundant collection of linear functionals. The redundancy is identified and removed, so the Vandermonde matrix represents a perfect pairing.
  DOI: https://doi.org/10.1007/978-3-030-55874-1_18

Ph.D. thesis

• Weights as degrees of freedom for high order Whitney finite elements (2022)
  Supervisors: Ana Alonso Rodríguez (Univeristà di Trento) and Francesca Rapetti (Université Côte d'Azur)
  High order Whitney forms, also known as trimmed polynomial di erential forms, are a celebrated family of di erential forms. They find their roots in Hassler Whitney’s book Geometric integration theory, published in 1957, where a low degree counterpart was used to prove the famous de Rham’s Theorem. It was only in the ’80s that they were recognised as a powerful tool in numerical analysis, when they were proved to parametrise Nédélec’s first family of finite elements. In Whitney’s spirit, one may choose weights, namely integrals of k-forms on k-simplices, as degrees of freedom for these spaces. To do this, the concept of small simplices shall be introduced. A small simplex is a piece of a (virtual) partitioning of a simplex. We show that weights associated with appropriate small simplices ensure unisolvence for Nédélec’s first family and we offer a strategy to shape the geometry of small simplices. This allows to generalise classical concepts peculiar to Lagrangian finite elements and Lagrangian interpolation to higher dimensional frameworks. The theory is flanked by numerical examples, relating results with the geometry of the problem.
  DOI: https://doi.org/10.70675/3b1f8819z26d7z4995zac79z0855fbdc8bb5

Preprints

• Bruni Bruno, L., Serra-Capizzano, S., On the conditioning of polynomial histopolation, (2026)
  The intrinsic exponential conditioning of the monomial basis is formalized. An orthogonal behavior of Chebyshev second family is shown. Consequences on the Euclidean and the Frobenius conditioning are discussed.
  Arxiv: https://arxiv.org/pdf/2511.15395

• Bruni Bruno, L., Cappellazzo, G., Erb, W., Karimnejad Esfahani, M., Scattered data histopolation in averaging kernel Hilbert spaces, (2026)
  The framework of histopolation is extended to kernel methods. The concept of averaging kernel Hilbert space is formalized.
  Arxiv: https://arxiv.org/pdf/2601.07967

• Bruni Bruno, L., Massa, P., Perracchione, E., Trombini, M., Greedy techniques for inverse problems, (2025)
  Greedy techniques for kernel interpolation are blended with regularization theory. Bounds are derived. Application to solar imaging is proposed: reconstructions are obtained by only few points in the Fourier domain.
  Arxiv: https://arxiv.org/pdf/2512.04046

• Bruni Bruno, L., Piazzon, F., Sampling, approximation and interpolation of differential forms by admissible integral k-meshes, (2025)
  Sampling inequalities are studied for differential forms. Introducing a concept of admissible k-mesh, improved convergence rates are offered, and Fekete currents are extracted as an application.
  Arxiv: https://arxiv.org/pdf/2504.05266

See my researchgate, google scholar or scopus.

Talks, seminars and lectures

• 2026: Jagiellonian University, SHARK26-FV (University of Coimbra), Università di Bologna, GNCS annual meeting, Università di Genova, Modern Kernel Methods and Applications (Honk Kong Baptist University)

• 2025: YAMC (Università di Padova), DRWAA25 (Università di Padova), SIMAI2025 (SISSA), Shanks conference - Constructive Functions (Vanderbilt University), Fast Methods for Isogeometric Analysis (INdAM), Politecnico di Torino, M2A25 (University of Marrakech)

• 2024: NAMAS24, DWCAA24 (Università di Padova), GIMC-SIMAI Young (Università di Napoli Federico II), RITA Young Researchers meeting, Università di Roma Tor Vergata

• 2023: SToK23 (Università di Camerino), DRWAA23 (Università di Padova), SuprenumPDE (EPFL), Due giorni di Algebra Lineare Numerica (GSSI), Software for Approximation 23 (Università di Torino), Università dell'Insubria

• 2022: ESCO 2022, Università di Padova, Università di Trento, Software for Approximation 2022 (Università di Torino)

• 2021: ICOSAHOM 2020+1 (TU Wien)

• 2019: Università di Trento, ENUMATH 2019

You can find some slides from my talks on the following research topics: histopolation, conditioning of histopolation matrices, spectral analysis of Whitney forms (see also this poster), weights for Whitney forms (see also the slides of my PhD defense), Lagrange interpolation of differential forms.