Quasi-interpolation by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml288" display="inline" overflow="scroll" altimg="si57.gif"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> quartic splines on type-1 triangulations

Barrera, D.; Dagnino, Catterina; Ibáñez, María; Remogna, Sara

doi:10.1016/j.cam.2018.08.005

Cited by 9 publications

(4 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Univariate point QIOs are useful tools to construct quadrature formulas both for (9) and for (10). In [25,28,29,35,[39][40][41][42] we generate integration rules based on the approximation of f in (9) or in (10) by point QI splines, we prove a very satisfactory error theory and we provide experimental results. By means of product of quadratures such as those obtained for (10), in [27] we construct and study cubature formulas for the numerical evaluation of the following CPV integral: 1) and ( 3), cubatures for the evaluation of integrals…”

Section: Numerical Integration and Differentiationmentioning

confidence: 99%

See 1 more Smart Citation

On spline quasi-interpolation through dimensions

Dagnino¹,

Lamberti²,

Remogna³

2022

Ann Univ Ferrara

Self Cite

View full text Add to dashboard Cite

The approximation of functions and data in one and high dimensions is an important problem in many mathematical and scientific applications. Quasi-interpolation is a general and powerful approximation approach having many advantages. This paper deals with spline quasi-interpolants and its aim is to collect the main results obtained by the authors, also in collaboration with other researchers, in such a topic through spline dimension, i.e. in the 1D, 2D and 3D setting, highlighting the approximation properties and the reconstruction of functions and data, the applications in numerical integration and differentiation and the numerical solution of integral and differential problems.

show abstract

Section: Numerical Integration and Differentiationmentioning

confidence: 99%

“…[55] and references therein) or by setting their Bernstein-Bézier coefficients to appropriate combinations of the given data values (see e.g. [6,8,9] and references therein), in the following we consider the use of locally supported spanning functions (see e.g. [14,21,55,60,72,82] and references therein).…”

Section: Spline Quasi-interpolating Operators In C R Smentioning

confidence: 99%

On spline quasi-interpolation through dimensions

Dagnino¹,

Lamberti²,

Remogna³

2022

Ann Univ Ferrara

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, on each square of the quadrangulation associated with the DEM the coefficients of the representation of the quasi-interpolant in terms of the corresponding Bernstein polynomials are directly defined from the values at the points in a neighborhood. [14][15][16][17] In Section 2 a nonstandard univariate quasi-interpolant is constructed for functions defined on the real line, endowed with a uniform partition. Some numerical tests are presented to show the performance of this kind of spline quasi-interpolant.…”

Section: Introductionmentioning

confidence: 99%

“…The nonstandard feature of the quasi‐interpolant constructed here comes from the fact that it will be a tensor product quasi‐interpolant defined from a univariate non‐standard quasi‐interpolant, which is constructed on each sub‐interval by providing the coefficients in the Bernstein basis. Therefore, on each square of the quadrangulation associated with the DEM the coefficients of the representation of the quasi‐interpolant in terms of the corresponding Bernstein polynomials are directly defined from the values at the points in a neighborhood 14–17 …”

Section: Introductionmentioning

confidence: 99%