# Teodora CatinasBabeş-Bolyai University | UBB · Department of Mathematics

Teodora Catinas

Professor

## About

46

Publications

2,864

Reads

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218

Citations

Citations since 2017

Additional affiliations

October 2000 - present

## Publications

Publications (46)

Fractional differential equations describe nature adequately because of the symmetry properties that describe physical and biological processes. In this paper, a new approximation is found for the variable-order (VO) Riemann-Liouville fractional derivative (RLFD) operator; on that basis, an efficient numerical approach is formulated for VO time-fra...

We consider two types of Cheney–Sharma operators for functions defined on a triangle with all straight sides. We construct their product and Boolean sum, we study their interpolation properties and the orders of accuracy and we give different expressions of the corresponding remainders, highlighting the symmetry between the methods. We also give so...

Starting with the classical, the modified and the iterative Shepard methods, we construct some new Shepard type operators, using the inverse quadratic and the inverse multiquadric radial basis functions. Given some sets of points, we compute some representative subsets of knot points following an algorithm described by J.R. McMahon in 1986.

We consider results regarding Bernstein and Cheney–Sharma-type operators that interpolate functions defined on triangles with straight and curved sides and we introduce a new Cheney–Sharma-type operator for the triangle with one curved side, highlighting the symmetry between the methods. We present some properties of the operators, their products a...

For solving the problem of modeling and visualization of scattered data that should preserve some constraints, we use a modified Shepard type operator that is required to fulfill some special conditions, highlighting the symmetry with other methods. We illustrate the properties of the obtained operators by some numerical examples.

"We obtain some new Shepard type operators based on the classical, the modi ed Shepard methods and the least squares thin-plate spline function. Given some sets of points, we compute some representative subsets of knot points following an algorithm described by J. R. McMahon in 1986."

We extend some Nielson type interpolation operators to the cases of standard and arbitrary triangles with one curved side. The correspondence between the operators defined on standard triangles and arbitrary triangles is made using barycentric coordinates. We study the interpolation properties of the obtained operators and the interpolation errors....

Using the weakly Picard operators technique and the contraction principle, we study the convergence of the iterates of some modified Bernstein type operators.

We construct some generalized Hermite-type interpolation operators for the case of a triangle with one curved side, and we consider their product and Boolean sum operators. We study the interpolation properties of these operators, the orders of accuracy and the remainders of the interpolation formulas. Finally, we give some numerical examples.

We extend some Cheney-Sharma type operators to a triangle with one curved side. We construct their product and Boolean sum, we study their interpolation properties, the orders of accuracy and we give different expressions of the corresponding remainders. We also give some illustrative examples.

We present some extensions of several interpolation operators introduced by R. E. Barnhill, J. A. Gregory and G. M. Nielson in [1], [2], to the case of a triangle with one curved side. We study their interpolation properties and the remainders of the corresponding interpolation formulas. We also present some product and Boolean sum operators and an...

We extend some Nielson and Marshall type interpolation operators to the case of a triangle with one curved side. We study the interpolation properties of the obtained operators and of their product and Boolean sum operators, the orders of accuracy and the remainders of the corresponding interpolation formulas. Finally, we give some numerical exampl...

We introduce an iterative modification of the combined Shepard operator of Bernoulli type, introduced in Cătinaş (Calcolo 44:189–202, 2007), that is free from artificial setup of parameters, and corresponds to successive scaling.

There are constructed some Cheney-Sharma type operators defined on a square with one curved side. They are extensions of the Cheney-Sharma type operators of second kind, given by E.W. Cheney and A. Sharma in [14], to the case of a curved sided domain. There are constructed the univariate Cheney-Sharma type operators, their product and boolean sum o...

Let Omega subset of R-p, p is an element of N* be a nonempty subset and B(Omega) be the Banach lattice of all bounded real functions on Omega, equipped with sup norm. Let X subset of B(Omega) be a linear sublattice of B(Omega) and A: X -> X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly...

We construct some classes of surfaces which satisfy some given conditions, using some Hermite, Nielson and Marshall type interpolation operators defined on a triangle with one curved side.

We consider some Bernstein-type operators as well as their product and Boolean sum for a function defined on a triangle with all curved sides. Using the weakly Picard operators technique and the contraction principle, we study the convergence of the iterates of these operators.

This paper contains a survey regarding interpolation and Bernstein-type operators defined on triangles having one or all curved sides; we consider as well some of the product and Boolean sum operators. We study the interpolation properties, the orders of accuracy and the remainders of the generated approximation formulas.

We use some interpolation operators and some Bernstein type operators for construction of surfaces which satisfy some given conditions.

Using the weakly Picard operators technique, we study the convergence of the iterates of some bivariate and trivariate Cheney-Sharma operators. Also, we generalize the procedure for the multivariate case.

We introduce an improved bivariate thin-plate spline quasi-interpolation operator obtained by means of Bernoulli bivariate oper-ator. We study this combined operator and give some error bounds in terms of the modulus of continuity of high order and also with Peano's theorem. Finally, we make extensive comparison with other existing methods and give...

Given a function defined on a square with one curved side, we consider some Bernstein-
type operators as well as their product and Boolean sum. Using the weakly Picard operators tech-
nique and the contraction principle, we study the convergence of the iterates of these operators.

We construct and analyze Bernstein-type operators on triangles with curved sides, their product and Boolean sum. We study the interpolation properties and approximation accuracy. Using the modulus of continuity we also study the remainders of the corresponding approximation formulas. Finally, there are given some particular cases and numerical exam...

We construct Bernstein-type operators on a triangle with one curved side. We study univariate operators, their product and
Boolean sum, as well as their interpolation properties, the order of accuracy (degree of exactness, precision set) and the
remainder of the corresponding approximation formulas. We also give some illustrative examples.
Mathema...

We construct certain Lagrange, Hermite and Birkhoff-type operators, which interpolate a given function and some of its derivatives
on the border of a triangle with one curved side, as well as some of their product and Boolean sum operators. We study the
interpolation properties and the order of accuracy (degree of exactness and precision set) of th...

We construct Lagrange, Hermite and Birkhoff-type operators, which interpolate a given function and some of its derivatives
on the border of a tetrahedron with three straight edges and three curved edges; we consider as well some of their product
and boolean sum operators. We study the interpolation properties and the order of accuracy of the constr...

We construct some Bernstein-type operators on a square with one and two curved sides, their product and Boolean sum. We study their interpolation properties, the orders of accuracy and the remainders of the corresponding approximation formulas. Finally, we give some numerical examples.

The method of Shepard is an efficient method for interpolation of very large scattered data sets; unfortunately, it has poor reproduction qualities and high computational cost. In this paper we introduce a new operator which diminishes these drawbacks. This operator results from the combination of the Shepard operator with a new interpolation opera...

In this survey paper it is studied the optimality in sense of
Nikolski for some classes of quadrature formulas, using the method of ϕ-
function. It is presented the one-to-one correspondence between ϕ-functions
and the quadrature formulas. Also, there are given some examples
of quadrature formulas which are optimal in sense of Nikolski with regard...

We extend the Shepard operator by combining it with the Lidstone bivariate operator. We study this combined operator and give some error bounds.

We study the bivariate Shepard-Lidstone interpolation operator and obtain new estimates for the remainder. Some numerical examples are provided. MSC 2000: 41A63, 41A80.

We consider the interpolation problem for some data on several nodes of a given triangle. We show that an interpolant may be found by dividing the initial problem into two subproblems, each one with some fewer nodes. The main result is given in Theorem 5.

We extend the Shepard operator by combining it with the Abel- Goncharov univariate operator in order to increase the degree of exactness and to use some specic functionals. We study this combined operator and give some of its properties. We introduce the corresponding interpolation formula and study its remainder term. MSC 2000. 65D05. Keywords. Sh...

We obtain tridimensional approximation operators considering the Boolean sum and the tensor product of the parametric extensions of some univariate operators. We extend univariate operators so they can operate on functions of three variables.

An efficient method for multivariate interpolation of very large scattered data sets is the method of Shepard. It has the advantages of a small storage requirement and an easy generalization to additional independent variables, but it suffers from no good reproduction quality, low accuracy and a high computational cost rela- tive to some alternativ...

## Projects

Project (1)

This Special Issue is mainly devoted to recent research results in numerical analysis, approximation theory (including multivariate interpolation), scientific computing, differential equations, and symmetries in the applied mathematics field. Numerical analysis and approximation theory are essential parts of the field of applied mathematics. They constitute fields of active research and continual development with applications to real life problems. For example, the results in domains such as wavelets, multivariate spline functions, radial functions, etc., have practical applications in the fields of computer aided design, geometric modelling, geodesy, image analysis, etc. The problem of the interpolation of arbitrarily spaced data is encountered in such areas as geology, cartography, earth sciences, etc. Symmetry methods also play an essential role in real world applications. Differential equations are essential tools for modeling different processes appearing in science. They give rise to important questions such as the existence and uniqueness of the solution, stability, numerical methods of approximation, symmetry methods of evolution equations, etc.
Details can be found at the following link:
https://www.mdpi.com/journal/symmetry/special_issues/numerical_analysis_approximation_theory