A5026527736- Advanced Numerical Analysis Techniques
- Mathematical functions and polynomials
- Numerical methods in engineering
- Iterative Methods for Nonlinear Equations
- Image and Signal Denoising Methods
- Advanced Numerical Methods in Computational Mathematics
- Mathematical Approximation and Integration
- Model Reduction and Neural Networks
- Matrix Theory and Algorithms
- Electromagnetic Scattering and Analysis
- Polynomial and algebraic computation
- Fractional Differential Equations Solutions
- Medical Image Segmentation Techniques
- Approximation Theory and Sequence Spaces
- Digital Filter Design and Implementation
- Advanced Mathematical Modeling in Engineering
- Numerical methods in inverse problems
- Advanced Image Processing Techniques
- Numerical Methods and Algorithms
- Electromagnetic Simulation and Numerical Methods
- Statistical and numerical algorithms
- Medical Imaging Techniques and Applications
- Probabilistic and Robust Engineering Design
- Characterization and Applications of Magnetic Nanoparticles
- Advanced Combinatorial Mathematics
University of Padua
2015-2024
Civita
2017-2024
Istituto Nazionale di Alta Matematica Francesco Severi
2022-2024
Florence (Netherlands)
2021
Collegio Carlo Alberto
2016
Polytechnic University of Turin
2012-2015
University of Verona
2001-2009
Politecnico di Milano
2002-2005
University of Udine
1997-2002
Centro di Ricerca in Matematica Pura ed Applicata
1995
We discuss and compare two greedy algorithms that compute discrete versions of Fekete-like points for multivariate compact sets by basic tools numerical linear algebra. The first gives the so-called approximate Fekete QR factorization with column pivoting Vandermonde-like matrices. second computes Leja LU row pivoting. Moreover, we study asymptotic distribution such when they are extracted from weakly admissible meshes.
In kernel-based approximation, it is well-known that the direct approach to interpolation prone ill-conditioning of matrix. One simple idea use other better-conditioned bases span same space translated kernels i.e. their associated native space. Pazouki and Schaback (2011) tracked this issue by investigating different factorization matrix in order build stable orthonormal for corresponding positive definite kernels. paper, we work with reproducing kernel K Hilbert NΦ(Ω) a conditionally Φ on...
It is often observed that interpolation based on translates of radial basis functions or non-radial kernels numerically unstable due to exceedingly large condition the kernel matrix. But if stability assessed in function space without considering special bases, this paper proves kernel-based stable. Provided data are not too wildly scattered, L 2 ∞ norms interpolants can be bounded above by discrete ℓ2 and ℓ data. Furthermore, Lagrange uniformly Lebesgue constants grow at most like square...
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications, such as medical imaging. In this paper, we study a radial basis function type of method scattered data that incorporates via variable scaling function. For the construction discontinuous kernel functions, information on edges interpolated is necessary. We characterize native space spanned by these error bounds terms fill distance node set. To extract location...
This paper proposes a Direct Rational Radial Basis Functions Partition of Unity (D-RRBF-PU) approach to compute derivatives functions with steep gradients or discontinuities. The novelty the method concerns how are approximated. More precisely, all partition unity weight eliminated while we local rational approximants in each patch. As result, approximate obtained more easily and quickly than those standard formulation. corresponding error bounds briefly discussed. Some numerical results...
We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points Leja Points. These provide new computational tools for polynomial least squares interpolation multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral high-order methods PDEs.
Abstract In this paper we address the problem of approximating functions with discontinuities via kernel-based methods. The main result is construction discontinuous basis functions. linear spaces spanned by these kernels lead to a very flexible tool which sensibly or completely reduces well-known Gibbs phenomenon in reconstructing jumps. For new provide error bounds and numerical results that support our claims. method also effectively tested for satellite images.