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Theory of quasi-orthogonal polynomials is significantly related to constructing vector Padé approximations. The present paper introduces an efficient procedure to compute adjacent families of quasi-orthogonal polynomials as defined in Sadaka (Appl. Numer. Math. 21:57–70, 1996) and Sadaka (Appl. Numer. Math. 24:483–499, 1997). The derived algorithm uses short recursive relations whose coefficients are written in terms of lower triangular block determinants. The strategy of computing such determinants is given and analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we combine the S-iteration process introduced by Agarwal et al. (J. Nonlinear Convex Anal., 8(1), 61–79 2007) with the proximal point algorithm introduced by Rockafellar (SIAM J. Control Optim., 14, 877–898 1976) to propose a new modified proximal point algorithm based on the S-type iteration process for approximating a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mappings in the framework of CAT(0) spaces and prove the △-convergence of the proposed algorithm for solving common minimization problem and common fixed point problem. Our result generalizes, extends and unifies the corresponding results of Dhompongsa and Panyanak (Comput. Math. Appl., 56, 2572–2579 2008), Khan and Abbas (Comput. Math. Appl., 61, 109–116 2011), Abbas et al. (Math. Comput. Modelling, 55, 1418–1427 2012) and many more. [ABSTRACT FROM AUTHOR]

We will refer to the paper "Convergence rates for Kaczmarz-type algorithms", published in Numerical Algorithms, 79(1)(2018), 1-17. It was observed by Dr. Mokhtar Abbasi (Department of Mathematics, University of Qom, Iran) that in the proof of Theorem 7, related to the linear convergence rate of the MREK algorithm it exists an inequality which is not always true. [ABSTRACT FROM AUTHOR]

The strong ℋ -tensors have important applications in many areas of science and engineering, e.g., the determination of positive definiteness for an even-order homogeneous polynomial form in the real field. In this paper, we propose two iterative algorithms with non-parameter for identifying strong ℋ -tensors, which overcome the drawback of choosing the best value of parameter 𝜖 in some existing algorithms given by Li et al. and Liu et al. (J. Comput. Appl. Math., 255, 1–14, 2014 and Comput. Appl. Math. 36, 1623–1635, 2017). Some numerical experiments are performed to illustrate the feasibility and effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool—pfaffians, instead of determinants in the paper. It turns out that Brezinski-Durbin-Redivo-Zaglia’s transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, we propose a segmentation method based on the generalized fast marching method (GFMM) developed by Carlini et al. (submitted). The classical fast marching method (FMM) is a very efficient method for front evolution problems with normal velocity (see also Epstein and Gage, The curve shortening flow. In: Chorin, A., Majda, A. (eds.) Wave Motion: Theory, Modelling and Computation, 1997) of constant sign. The GFMM is an extension of the FMM and removes this sign constraint by authorizing time-dependent velocity with no restriction on the sign. In our modelling, the velocity is borrowed from the Chan–Vese model for segmentation (Chan and Vese, IEEE Trans Image Process 10(2):266–277, 2001). The algorithm is presented and analyzed and some numerical experiments are given, showing in particular that the constraints in the initialization stage can be weakened and that the GFMM offers a powerful and computationally efficient algorithm. [ABSTRACT FROM AUTHOR]

Abstract  This paper is devoted to multiresolution schemes that use a stencil selection procedure in order to obtain adaptation to the presence of edges in the images. Since non adapted schemes, based on a centered stencil, are less affected by the presence of texture, we propose the introduction of some weight that leads to a more frequent use of the centered stencil in regions without edges. In these regions the different stencils have similar weights and therefore the selection becomes an ill-posed problem with high risk of instabilities. In particular, numerical artifacts appear in the decompressed images. Our attention is centered in ENO schemes, but similar ideas can be developed for other multiresolution schemes. A nonlinear multiresolution scheme corresponding to a nonlinear interpolatory technique is analyzed. It is based on a modification of classical ENO schemes. As the original ENO stencil selection, our algorithm chooses the stencil within a region of smoothness of the interpolated function if the jump discontinuity is sufficiently big. The scheme is tested, allowing to compare its performances with other linear and nonlinear schemes. The algorithm gives results that are at least competitive in all the analyzed cases. The problems of the original ENO interpolation with the texture of real images seem solved in our numerical experiments. Our modified ENO multiresolution will lead to a reconstructed image free of numerical artifacts or blurred regions, obtaining similar results than WENO schemes. Similar ideas can be used in multiresolution schemes based in other stencil selection algorithms. [ABSTRACT FROM AUTHOR]