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Héctor Orera

Publications and source records attributed to Héctor Orera.

5 recordsLinked to original sources
arXiv2025

An evaluation algorithm for q-Bézier triangular patches formed by convex combinations

An extension to triangular domains of the univariate q-Bernstein basis functions is introduced and analyzed. Some recurrence relations and properties such as partition of unity and degree elevation are proved for them. It is also proved that they form a basis for the space of polynomials of total degree less than or equal to n on a triangle. In addition, it is presented a de Casteljau type evaluation algorithm whose steps are all linear convex combinations.

math.NA↗
arXiv2025

Optimal properties of tensor product of B-bases

It is proved the optimal conditioning for the infinity norm of collocation matrices of the tensor product of normalized B-bases among the tensor product of all normalized totally positive bases of the corresponding space of functions. Bounds for the minimal eigenvalue and singular value and illustrative numerical examples are also included.

math.NA↗
arXiv2025

Accurate algorithms for Bessel matrices

In this paper, we prove that any collocation matrix of Bessel polynomials at positive points is strictly totally positive, that is, all its minors are positive. Moreover, an accurate method to construct the bidiagonal factorization of these matrices is obtained and used to compute with high relative accuracy the eigenvalues, singular values and inverses. Similar results for the collocation matrices for the reverse Bessel polynomials are also obtained. Numerical examples illustrating the theoretical results are included.

math.NA↗
arXiv2025

Infinity norm bounds for the inverse of Nekrasov matrices using scaling matrices

For many applications, it is convenient to have good upper bounds for the norm of the inverse of a given matrix. In this paper, we obtain such bounds when A is a Nekrasov matrix, by means of a scaling matrix transforming A into a strictly diagonally dominant matrix. Numerical examples and comparisons with other bounds are included. The scaling matrices are also used to derive new error bounds for the linear complementarity problems when the involved matrix is a Nekrasov matrix. These error bounds can improve considerably other previous bounds.

math.NA↗