Prof. Dr. Stefano De Marchi
Mathematics, University of Padua, Padua, Italy
'%3e%3cpath%20d='M22.1642%2019.0924C21.7317%2018.068%2021.1041%2017.1375%2020.3163%2016.3527C19.5309%2015.5656%2018.6006%2014.9381%2017.5766%2014.5048C17.5674%2014.5002%2017.5582%2014.4979%2017.5491%2014.4933C18.9774%2013.4616%2019.9059%2011.7811%2019.9059%209.88504C19.9059%206.74408%2017.3611%204.19922%2014.2201%204.19922C11.0792%204.19922%208.53429%206.74408%208.53429%209.88504C8.53429%2011.7811%209.46282%2013.4616%2010.8912%2014.4956C10.882%2014.5002%2010.8728%2014.5025%2010.8636%2014.5071C9.83652%2014.9404%208.91487%2015.5617%208.1239%2016.355C7.33685%2017.1404%206.70933%2018.0707%206.276%2019.0947C5.85031%2020.0972%205.62072%2021.172%205.59967%2022.2609C5.59905%2022.2853%205.60335%2022.3097%205.61229%2022.3325C5.62123%2022.3553%205.63465%2022.376%205.65174%2022.3935C5.66883%2022.4111%205.68926%2022.425%205.71182%2022.4345C5.73437%2022.444%205.7586%2022.4489%205.78308%2022.4489H7.15868C7.25956%2022.4489%207.3398%2022.3686%207.3421%2022.2701C7.38795%2020.5001%208.09868%2018.8425%209.35506%2017.5861C10.655%2016.2862%2012.3814%2015.5709%2014.2201%2015.5709C16.0588%2015.5709%2017.7852%2016.2862%2019.0852%2017.5861C20.3415%2018.8425%2021.0523%2020.5001%2021.0981%2022.2701C21.1004%2022.3709%2021.1807%2022.4489%2021.2815%2022.4489H22.6571C22.6816%2022.4489%2022.7058%2022.444%2022.7284%2022.4345C22.751%2022.425%2022.7714%2022.4111%2022.7885%2022.3935C22.8056%2022.376%2022.819%2022.3553%2022.8279%2022.3325C22.8369%2022.3097%2022.8412%2022.2853%2022.8406%2022.2609C22.8176%2021.165%2022.5907%2020.0989%2022.1642%2019.0924ZM14.2201%2013.8284C13.1678%2013.8284%2012.1773%2013.418%2011.4322%2012.6729C10.6871%2011.9278%2010.2767%2010.9374%2010.2767%209.88504C10.2767%208.83271%2010.6871%207.84227%2011.4322%207.09715C12.1773%206.35204%2013.1678%205.94165%2014.2201%205.94165C15.2724%205.94165%2016.2629%206.35204%2017.008%207.09715C17.7531%207.84227%2018.1635%208.83271%2018.1635%209.88504C18.1635%2010.9374%2017.7531%2011.9278%2017.008%2012.6729C16.2629%2013.418%2015.2724%2013.8284%2014.2201%2013.8284Z'%20fill='%238590A2'/%3e%3c/g%3e%3c/svg%3e)
Co-authors
Following
Followers
Research Focus & Metrics
Explore full metrics on Scilit
Academic Career Length
34Years (1993-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications1 October 2005 in Advances in Computational Mathematics
Journal Article
1 November 2006 in Journal of Approximation Theory
Journal Article
LBLen Bos
Len Bos
MCMarco Caliari
Marco CaliariStefano De MarchiMVMarco Vianello
Marco Vianello
YXYuan Xu
Yuan Xu
1 January 2010 in SIAM Journal on Numerical Analysis
Journal Article
We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools of numerical linear algebra. The first gives the so-called approximate Fekete points by QR factorization with column pivoting of Vandermonde-like matrices. The second computes discrete Leja points by LU factorization with row pivoting. Moreover, we study the asymptotic distribution of such points when they are extracted from weakly admissible meshes.
12 August 2008 in Advances in Computational Mathematics
Journal Article
Stefano De MarchiRSRobert Schaback
Robert Schaback
It is often observed that interpolation based on translates of radial basis functions or non-radial kernels is numerically unstable due to exceedingly large condition of the kernel matrix. But if stability is assessed in function space without considering special bases, this paper proves that kernel-based interpolation is stable. Provided that the data are not too wildly scattered, the L 2 or L ∞ norms of interpolants can be bounded above by discrete ℓ2 and ℓ ∞ norms of the data. Furthermore, Lagrange basis functions are uniformly bounded and Lebesgue constants grow at most like the square root of the number of data points. However, this analysis applies only to kernels of limited smoothness. Numerical examples support our bounds, but also show that the case of infinitely smooth kernels must lead to worse bounds in future work, while the observed Lebesgue constants for kernels with limited smoothness even seem to be independent of the sample size and the fill distance.
1 June 2005 in Applied Mathematics and Computation
Journal Article
1 December 2013 in Journal of Computational and Applied Mathematics
Journal Article
Stefano De MarchiGSGabriele Santin
Gabriele SantinAbout Me
Prof. Dr. Stefano De Marchi received his Laurea in Mathematics (1987), Master in Applied Mathematics (1991), and Ph.D. in Computational Mathematics (1994) from the University of Padova. He worked as an Assistant Professor of Numerical Analysis, University of Udine (1995–2001). In 2001, he moved to the University of Verona as an Assistant Professor, habilitated in 2017, and became a Full Professor of Numerical Analysis at the Department of Mathematics “Tullio Levi-Civita”, University of Padua in 2022. He is a fellow of INdAM-Gruppo Nazionale di Calcolo Scientico and UMI (Unione Matematica Italiana). He has made many important contributions to multivariate approximation theory, such as optimal points for polynomial interpolation of total degree, weakly admissible meshes, barycentric rational interpolation, stability and greedy algorithms in RBF approximation, rational RBF approximation, and medical image reconstruction. He is one of the discoverers of the so-called Padua points. For more details, see www.math.unipd.it/~demarchi.