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Your search keyword '"Trillo, J. C."' showing total 12 results
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12 results on '"Trillo, J. C."'

2. Geometric representation of the weighted harmonic mean of $n$ positive values and potential uses

Author

Amat, S., Ortiz, P., Ruiz, J., Trillo, J. C., and Yañez, D. F.

Subjects
Mathematics - Numerical Analysis, 41A05, 41A10, 65D17
Abstract

This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that will allow us to define numerical approximation methods in several dimensions adapted to discontinuities., Comment: 21 pages, 4 figures

Published
2022

3. A nonlinear PPH-type reconstruction based on equilateral triangles

Author

Amat, S., Ortiz, P., Ruiz, J., Trillo, J. C., and Yañez, D. F.

Subjects
Mathematics - Numerical Analysis, 41A05, 41A10, 65D17
Abstract

In this paper we introduce a new nonlinear reconstruction operator over two dimensional triangularized domains with equilateral triangles. We focus on the local definition of the operator. The ideas behind this definition come from some basic properties of the Harmonic mean of three positive values. We prove some results regarding the approximation properties of the operator and we carry out some numerical tests giving evidence of the avoidance of any Gibbs effects., Comment: 12 pages, 3 figures

Published
2022

9. On the use of generalized harmonic means in image processing using multiresolution algorithms.

Author

Amat, S., Magreñán, A. A., Ruiz, J., Trillo, J. C., and Yáñez, D. F.

Subjects
IMAGE processing, NONLINEAR operators, ARITHMETIC mean, ALGORITHMS, IMAGE compression, MATHEMATICS
Abstract

In this paper we design a family of cell-average nonlinear prediction operators that make use of the generalized harmonic means and we apply the resulting schemes to image processing. The new family of nonlinear schemes conserve the numerical properties of the linear schemes, such as the L 1 -stability, the order of accuracy or compression rate but avoiding Gibbs phenomenon close to the discontinuities. The generalized harmonic mean was introduced in the framework of point-values in [A. Guessab, M. Moncayo, and G. Schmeisser, A class of nonlinear four-point subdivision schemes. Properties in terms of conditions, Adv. Comput. Math. 37 (2012), pp. 151–190] in order to improve the results of the harmonic mean. However, in the cell-average setting our conclusion is that, from a numerical point of view, the advantage of using the new mean is not clear. [ABSTRACT FROM AUTHOR]

Published
2020
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