27 citations · 44 across the 20 of their papers we have counts for
25 papers
Paths of Stochastic Processes: a Sudden Turnaround
Robert Schaback, Emilio Porcu
The commonly accepted definition of paths starts from a random field but ignores the problem of setting joint distributions of infinitely many random variables for defining paths p…
Optimal Compactly Supported Functions in Sobolev Spaces
Robert Schaback
This paper constructs unique compactly supported functions in Sobolev spaces that have minimal norm, maximal support, and maximal central value, under certain renormalizations. The…
Greedy Adaptive Local Recovery of Functions in Sobolev Spaces
Robert Schaback
There are many ways to upsample functions from multivariate scattered data locally, using only a few neighbouring data points of the evaluation point. The position and number of th…
The Matérn Model: A Journey through Statistics, Numerical Analysis and Machine Learning
Emilio Porcu, Moreno Bevilacqua, Robert Schaback +1
The Matérn model has been a cornerstone of spatial statistics for more than half a century. More recently, the Matérn model has been central to disciplines as diverse as numerical…
Scaling of Radial Basis Functions
Elisabeth Larsson, Robert Schaback
This paper studies the influence of scaling on the behavior of Radial Basis Function interpolation. It focuses on certain central aspects, but does not try to be exhaustive. The mo…
Small Errors Imply Large Instabilities
Robert Schaback
Numerical Analysts and scientists working in applications often observe that once they improve their techniques to get a better accuracy, some instability creeps in through the bac…
On COVID-19 Modelling
Robert Schaback
This contribution analyzes the COVID-19 outbreak by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country…
Modelling Recovered Cases and Death Probabilities for the COVID-19 Outbreak
Robert Schaback
From March 23rd, the data for the recovered cases of COVID-19 are missing from the standard repository maintained by the Johns Hopkins University in collaboration with the WHO. But…
A Greedy Method for Solving Classes of PDE Problems
Robert Schaback
Motivated by the successful use of greedy algorithms for Reduced Basis Methods, a greedy method is proposed that selects N input data in an asymptotically optimal way to solve well…
An Approximation Theorist's View on Solving Operator Equations
Robert Schaback
When an Approximation Theorist looks at well-posed PDE problems or operator equations, and standard solution algorithms like Finite Elements, Rayleigh-Ritz or Trefftz techniques, m…
A Nonlinear Discretization Theory for Meshfree Collocation Methods applied to Quasilinear Elliptic Equations
Klaus Böhmer, Robert Schaback
We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is…
--Convergence of least-squares kernel collocation methods
Ka-Chun Cheung, Leevan Ling, Robert Schaback
The strong-form asymmetric kernel-based collocation method, commonly referred to as the Kansa method, is easy to implement and hence is widely used for solving engineering problems…
A Meshfree Method for Solving the Monge-Ampère Equation
Klaus Böhmer, Robert Schaback
This paper solves the two-dimensional Dirichlet problem for the Monge-Ampère equation by a strong meshless collocation technique that uses a polynomial trial space and collocation…
A Simple Solution for Maximum Range Flight
Robert Schaback
Within the standard framework of quasi-steady flight, this paper derives a speed that realizes the maximal obtainable range per unit of fuel. If this speed is chosen at each instan…
On the Fractional Derivatives of Radial Basis Functions
Maryam Mohammadi, Robert Schaback
The paper provides the fractional integrals and derivatives of the Rie\-mann-Liouville and Caputo type for the five kinds of radial basis functions (RBFs), including the powers, Ga…
Adaptive Approximation of Functions with Discontinuities
Licia Lenarduzzi, Robert Schaback
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth…
Error Analysis of Nodal Meshless Methods
Robert Schaback
There are many application papers that solve elliptic boundary value problems by meshless methods, and they use various forms of generalized stiffness matrices that approximate der…
Optimal Stencils in Sobolev Spaces
Oleg Davydov, Robert Schaback
This paper proves that the approximation of pointwise derivatives of order of functions in Sobolev space by linear combinations of function values cannot have a c…
Minimal Numerical Differentiation Formulas
Oleg Davydov, Robert Schaback
We investigate numerical differentiation formulas on irregular centers in two or more variables that are exact for polynomials of a given order and minimize an absolute seminorm of…
Superconvergence of Kernel-Based Interpolation
Robert Schaback
It is well-known that univariate cubic spline interpolation, if carried out on point sets with fill distance , converges only like in for functions in…
Approximation of Eigenfunctions in Kernel-based Spaces
Gabriele Santin, Robert Schaback
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the "native" Hilbert space $\calh$ in which they are reproducing. Continuous…
All Well--Posed Problems have Uniformly Stable and Convergent Discretizations
Robert Schaback
This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery pro…
Solving Heat Conduction Problems by the Direct Meshless Local Petrov-Galerkin (DMLPG) method
Davoud Mirzaei, Robert Schaback
As an improvement of the Meshless Local Petrov-Galerkin (MLPG), the Direct Meshless Local Petrov-Galerkin (DMLPG) method is applied here to the numerical solution of transient heat…
Direct meshless local Petrov-Galerkin (DMLPG) method: A generalized MLS approximation
Davoud Mirzaei, Robert Schaback
The Meshless Local Petrov{Galerkin (MLPG) method is one of the popular meshless methods that has been used very successfully to solve several types of boundary value problems since…