A Note on the Stability of ENO Multiresolution. - Sergio Amat; Sonia Busquier (Int. J. Comput. Math., 2002)

Tensor product multiresolution analysis with error control for compact image representation. - Sergio Amat; Francesc Aràndiga; Albert Cohen 002; Rosa Donat (Signal Process., 2002)

Nonseparable multiresolution with error control. - Sergio Amat (Appl. Math. Comput., 2003)

On a higher order Secant method. - Sergio Amat; Sonia Busquier (Appl. Math. Comput., 2003)

A modified secant method for semismooth equations. - Sergio Amat; Sonia Busquier (Appl. Math. Lett., 2003)

A fast Chebyshev's method for quadratic equations. - Sergio Amat; Sonia Busquier; Dhafer El Kebir; José Molina (Appl. Math. Comput., 2004)

Dynamics of a family of third-order iterative methods that do not require using second derivatives. - Sergio Amat; Sonia Busquier; Sergio Plaza (Appl. Math. Comput., 2004)

On the local convergence of secant-type methods. - Sergio Amat; Sonia Busquier; José Manuel Gutiérrez Jiménez (Int. J. Comput. Math., 2004)

Constructing attracting periodic orbits of three third-order iterative methods. - Sergio Amat; Sonia Busquier; Sergio Plaza (Appl. Math. Comput., 2005)

On a Steffensen's type method and its behavior for semismooth equations. - Sergio Amat; Sonia Busquier (Appl. Math. Comput., 2006)

Point Values Hermite Multiresolution for Non-smooth Noisy Signals. - I. Ali; Sergio Amat; Juan Carlos Trillo (Computing, 2006)

Analysis of a New Nonlinear Subdivision Scheme. Applications in Image Processing. - Sergio Amat; Rosa Donat; Jacques Liandrat; Juan Carlos Trillo (Found. Comput. Math., 2006)

A fully adaptive multiresolution scheme for image processing. - Sergio Amat; Rosa Donat; Jacques Liandrat; Juan Carlos Trillo (Math. Comput. Model., 2007)

On multiresolution schemes using a stencil selection procedure: applications to ENO schemes. - Sergio Amat; Sonia Busquier; Juan Carlos Trillo (Numer. Algorithms, 2007)

On the dynamics of the Euler iterative function. - Sergio Amat; Concepción Bermúdez; Sonia Busquier; Sergio Plaza (Appl. Math. Comput., 2008)

A modified Chebyshev's iterative method with at least sixth order of convergence. - Sergio Amat; Miguel Ángel Hernández-Verón; Natalia Romero Álvarez (Appl. Math. Comput., 2008)

linfinity-Stability for linear multiresolution algorithms: A new explicit approach. Part I: The basic rules and the Daubechies case. - Sergio Amat; María Moncayo (Appl. Math. Comput., 2008)

linfinity-Stability for linear multiresolution algorithms: A new explicit approach. Part II: The cases of Symlets, Coiflets, biorthogonal wavelets and supercompact multiwavelets. - Sergio Amat; María Moncayo (Appl. Math. Comput., 2008)

linfinity-Stability for linear multiresolution algorithms: A new explicit approach. Part III: The 2-D case. - Sergio Amat; María Moncayo (Appl. Math. Comput., 2008)

High order iterative schemes for quadratic equations. - Virginia Alarcón; Sergio Amat; Sonia Busquier; Fernando Manzano (Numer. Algorithms, 2008)

On the dynamics of some Newton's type iterative functions. - Sergio Amat; Concepción Bermúdez; Sonia Busquier; P. Leauthier; Sergio Plaza (Int. J. Comput. Math., 2009)

Exact error bounds for the reconstruction processes using interpolating wavelets. - Sergio Amat; María Moncayo (Math. Comput. Simul., 2009)

On a class of L1-stable nonlinear cell-average multiresolution schemes. - Sergio Amat; Karine Dadourian; Jacques Liandrat; Juan Ruiz 001; Juan Carlos Trillo (J. Comput. Appl. Math., 2010)

A family of stable nonlinear nonseparable multiresolution schemes in 2D. - Sergio Amat; Karine Dadourian; Jacques Liandrat; Juan Ruiz 001; Juan Carlos Trillo (J. Comput. Appl. Math., 2010)

Non-uniform multiresolution analysis with supercompact multiwavelets. - Sergio Amat; María Moncayo (J. Comput. Appl. Math., 2010)

Fast Multiresolution Algorithms and Their Related Variational Problems for Image Denoising. - Sergio Amat; Juan Ruiz 001; Juan Carlos Trillo (J. Sci. Comput., 2010)

On a third-order Newton-type method free of bilinear operators. - Sergio Amat; Concepción Bermúdez; Sonia Busquier; Sergio Plaza (Numer. Linear Algebra Appl., 2010)

Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms. - Sergio Amat; Karine Dadourian; Jacques Liandrat (Adv. Comput. Math., 2011)

Third-order iterative methods with applications to Hammerstein equations: A unified approach. - Sergio Amat; Sonia Busquier; José Manuel Gutiérrez Jiménez (J. Comput. Appl. Math., 2011)

Error bounds for a class of subdivision schemes based on the two-scale refinement equation. - María Moncayo; Sergio Amat (J. Comput. Appl. Math., 2011)

A wavelet adaptive two-step Newton type method. - Sergio Amat; Sonia Busquier; Antonio Escudero; Fernando Manzano (J. Frankl. Inst., 2011)

Tight numerical bounds for digital terrain modeling by interpolatory subdivision schemes. - María Moncayo; J. F. Reinoso; Sergio Amat (Math. Comput. Simul., 2011)

On a nonlinear subdivision scheme avoiding Gibbs oscillations and converging towards Cs functions with s>1. - Sergio Amat; Karine Dadourian; Jacques Liandrat (Math. Comput., 2011)

On two families of high order Newton type methods. - Sergio Amat; Sonia Busquier; Concepción Bermúdez; Sergio Plaza (Appl. Math. Lett., 2012)

On a Newton-Type Method for Differential-Algebraic Equations. - Sergio Amat; María José Legaz; Pablo Pedregal (J. Appl. Math., 2012)

On a compact non-extrapolating scheme for adaptive image interpolation. - Sergio Amat; Jacques Liandrat; Juan Ruiz 001; Juan Carlos Trillo (J. Frankl. Inst., 2012)

Adaptive interpolation of images using a new nonlinear cell-average scheme. - Sergio Amat; Juan Ruiz 001; Juan Carlos Trillo (Math. Comput. Simul., 2012)

Reciprocal polynomial extrapolation vs Richardson extrapolation for singular perturbed boundary problems. - Sergio Amat; Sonia Busquier; María José Legaz; Fernando Manzano; Juan Ruiz 001 (Numer. Algorithms, 2012)

Nonlinear thresholding of multiresolution decompositions adapted to the presence of discontinuities. - Sergio Amat; Jacques Liandrat (Adv. Comput. Math., 2013)

On a bilinear operator free third order method on Riemannian manifolds. - Sergio Amat; Ioannis K. Argyros; Sonia Busquier; Rodrigo A. Castro; Saïd Hilout; Sergio Plaza (Appl. Math. Comput., 2013)

Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications. - Sergio Amat; Sonia Busquier; Àngela Grau; Miquel Grau-Sánchez (Appl. Math. Comput., 2013)

Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators. - Sergio Amat; Rosa Donat; Juan Carlos Trillo (Appl. Math. Comput., 2013)

On a two-step relaxed Newton-type method. - Sergio Amat; Ángel Alberto Magreñán; Natalia Romero Álvarez (Appl. Math. Comput., 2013)

High order nonlinear interpolatory reconstruction operators and associated multiresolution schemes. - Sergio Amat; Karine Dadourian; Jacques Liandrat; Juan Carlos Trillo (J. Comput. Appl. Math., 2013)

On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods. - Miquel Grau-Sánchez; Miquel Noguera; Sergio Amat (J. Comput. Appl. Math., 2013)

Newton-type methods on Riemannian manifolds under Kantorovich-type conditions. - Sergio Amat; Ioannis K. Argyros; Sonia Busquier; Rodrigo A. Castro; Saïd Hilout; Sergio Plaza (Appl. Math. Comput., 2014)

Improving the applicability of the secant method to solve nonlinear systems of equations. - Sergio Amat; Miguel Ángel Hernández-Verón; M. Jóse Rubio (Appl. Math. Comput., 2014)

Third-order methods on Riemannian manifolds under Kantorovich conditions. - Sergio Amat; Sonia Busquier; Rodrigo A. Castro; Sergio Plaza (J. Comput. Appl. Math., 2014)

Expanding the Applicability of High-Order Traub-Type Iterative Procedures. - Sergio Amat; Ioannis K. Argyros; Sonia Busquier; Saïd Hilout (J. Optim. Theory Appl., 2014)

Improving the compression rate versus L 1 error ratio in cell-average error control algorithms. - Sergio Amat; Juan Ruiz 001; Juan Carlos Trillo (Numer. Algorithms, 2014)

Approximation of inverse operators by a new family of high-order iterative methods. - Sergio Amat; José Antonio Ezquerro; Miguel Ángel Hernández-Verón (Numer. Linear Algebra Appl., 2014)

On a family of high-order iterative methods under gamma conditions with applications in denoising. - Sergio Amat; Miguel Ángel Hernández 001; Natalia Romero Álvarez (Numerische Mathematik, 2014)

Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators. - Sergio Amat; Sonia Busquier; Concepción Bermúdez; Ángel Alberto Magreñán (Algorithms, 2015)

Unifying the Classical Approach with New Technologies: An Innovative Proposal for Teaching Mathematics in Engineering. - Sergio Amat; Sonia Busquier; María José Legaz; Juan Ruiz 001 (Int. J. Interact. Multim. Artif. Intell., 2015)

A variable step-size implementation of a variational method for stiff differential equations. - Sergio Amat; María José Legaz; Pablo Pedregal (Math. Comput. Simul., 2015)

On a family of nonlinear cell-average multiresolution schemes for image processing: An experimental study. - Sergio Amat; Jacques Liandrat; Juan Ruiz 001; Juan Carlos Trillo (Math. Comput. Simul., 2015)

On a new family of high-order iterative methods for the matrix pth root. - Sergio Amat; J. A. Ezquerro; M. A. Hernández-Verón (Numer. Linear Algebra Appl., 2015)

A Steffensen type method of two steps in Banach spaces with applications. - Sergio Amat; Sonia Busquier; J. A. Ezquerro; M. A. Hernández-Verón (J. Comput. Appl. Math., 2016)

On an efficient k-step iterative method for nonlinear equations. - Sergio Amat; Concepción Bermúdez; M. A. Hernández-Verón; Eulalia Martínez (J. Comput. Appl. Math., 2016)

On a nonlinear mean and its application to image compression using multiresolution schemes. - Sergio Amat; Jacques Liandrat; Juan Ruiz 001; Juan Carlos Trillo (Numer. Algorithms, 2016)

Expanding the Applicability of Some High Order Househölder-Like Methods. - Sergio Amat; Ioannis K. Argyros; Miguel Ángel Hernández 001; Natalia Romero Álvarez (Algorithms, 2017)

On the Efficiency of a Family of Steffensen-Like Methods with Frozen Divided Differences. - Sergio Amat; Sonia Busquier; Miquel Grau-Sánchez; Miguel Ángel Hernández-Verón (Comput. Methods Appl. Math., 2017)

Wavelets for the Maxwell's equations: An overview. - Sergio Amat; Pedro J. Blázquez Tobías; Sonia Busquier; Concepción Bermúdez (J. Comput. Appl. Math., 2017)

New WENO Smoothness Indicators Computationally Efficient in the Presence of Corner Discontinuities. - Sergio Amat; Juan Ruiz 001 (J. Sci. Comput., 2017)

Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions. - Sergio Amat; Ioannis K. Argyros; Sonia Busquier; Ángel Alberto Magreñán (Numer. Algorithms, 2017)

On the convergence of a local third order shock capturing method for hyperbolic conservation laws. - Sergio Amat; Vicente F. Candela (Numer. Algorithms, 2017)

On a Power WENO Scheme with Improved Accuracy Near Discontinuities. - Sergio Amat; Jacques Liandrat; Juan Ruiz 001; Juan Carlos Trillo (SIAM J. Sci. Comput., 2017)

On a nonlinear 4-point ternary and non-interpolatory subdivision scheme eliminating the Gibbs phenomenon. - Sergio Amat; A. Choutri; Juan Ruiz 001; Sofiane Zouaoui (Appl. Math. Comput., 2018)

Analysis of the Gibbs phenomenon in stationary subdivision schemes. - Sergio Amat; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (Appl. Math. Lett., 2018)

On the local convergence study for an efficient k-step iterative method. - Sergio Amat; Ioannis K. Argyros; Sonia Busquier; M. A. Hernández-Verón; Eulalia Martínez (J. Comput. Appl. Math., 2018)

On an New Algorithm for Function Approximation with Full Accuracy in the Presence of Discontinuities Based on the Immersed Interface Method. - Sergio Amat; Zhilin Li 002; Juan Ruiz 001 (J. Sci. Comput., 2018)

On a class of three points cell-average multiresolution schemes. - Sergio Amat; Jacques Liandrat; María Moncayo; Juan Ruiz 001; Juan Carlos Trillo (Math. Comput. Simul., 2018)

On two high-order families of frozen Newton-type methods. - Sergio Amat; Ioannis K. Argyros; Sonia Busquier; M. A. Hernández-Verón (Numer. Linear Algebra Appl., 2018)

On a stable family of four-point nonlinear subdivision schemes eliminating the Gibbs phenomenon. - Sergio Amat; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (J. Comput. Appl. Math., 2019)

An efficient optimal family of sixteenth order methods for nonlinear models. - Ramandeep Behl; Sergio Amat; Ángel Alberto Magreñán; Sandile Sydney Motsa (J. Comput. Appl. Math., 2019)

On an algorithm to adapt spline approximations to the presence of discontinuities. - Sergio Amat; Juan Ruiz 001; Juan Carlos Trillo (Numer. Algorithms, 2019)

On New Strategies to Control the Accuracy of WENO Algorithms Close to Discontinuities. - Sergio Amat; Juan Ruiz 001; Chi-Wang Shu (SIAM J. Numer. Anal., 2019)

On a new WENO algorithm of order 2r with improved accuracy close to discontinuities. - Sergio Amat; Juan Ruiz 001; Chi-Wang Shu (Appl. Math. Lett., 2020)

Corrected approximation strategy for piecewise smooth bivariate functions. - Sergio Amat; David Levin; Juan Ruiz-Álvarez 001 (CoRR, 2020)

Corrected subdivision approximation of piecewise smooth functions. - Sergio Amat; David Levin; Juan Ruiz-Álvarez 001 (CoRR, 2020)

On the use of generalized harmonic means in image processing using multiresolution algorithms. - Sergio Amat; Ángel Alberto Magreñán; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (Int. J. Comput. Math., 2020)

On the application of Lehmer means in signal and image processing. - Sergio Amat; Ángel Alberto Magreñán; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (Int. J. Comput. Math., 2020)

On the local and semilocal convergence of a parameterized multi-step Newton method. - Sergio Amat; Ioannis K. Argyros; Sonia Busquier; M. A. Hernández-Verón; Dionisio F. Yáñez (J. Comput. Appl. Math., 2020)

On a family of non-oscillatory subdivision schemes having regularity Cr with r > 1. - Sergio Amat; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (Numer. Algorithms, 2020)

A New WENO-2r Algorithm with Progressive Order of Accuracy Close to Discontinuities. - Sergio Amat; Juan Ruiz 001; Chi-Wang Shu; Dionisio F. Yáñez (SIAM J. Numer. Anal., 2020)

Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing. - Sergio Amat; Juan Ruiz-Álvarez 001; Chi-Wang Shu; Dionisio F. Yáñez (Appl. Math. Comput., 2021)

Explicit multivariate approximations from cell-average data. - Sergio Amat; David Levin; Juan Ruiz-Álvarez 001; Dionisio F. Yáñez (Adv. Comput. Math., 2022)

Global and explicit approximation of piecewise smooth 2D functions from cell-average data. - Sergio Amat; David Levin; Juan Ruiz-Álvarez 001; Dionisio F. Yáñez (CoRR, 2022)

A nonlinear PPH-type reconstruction based on equilateral triangles. - Sergio Amat; Pedro Ortiz; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (CoRR, 2022)

Geometric representation of the weighted harmonic mean of n positive values and potential uses. - Sergio Amat; P. Ortiz; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (CoRR, 2022)

Numerical integration rules with improved accuracy close to singularities. - Sergio Amat; Zhilin Li 002; Juan Ruiz-Álvarez 001; Concepcion Solano; Juan Carlos Trillo (CoRR, 2022)

A class of C2 quasi-interpolating splines free of Gibbs phenomenon. - Sergio Amat; David Levin; Juan Ruiz-Álvarez 001; Juan Carlos Trillo; Dionisio F. Yáñez (Numer. Algorithms, 2022)

On the approximation of derivative values using a WENO algorithm with progressive order of accuracy close to discontinuities. - Sergio Amat; Juan Ruiz-Álvarez 001; Chi-Wang Shu; Dionisio F. Yáñez (Comput. Appl. Math., 2022)

Numerical integration rules with improved accuracy close to discontinuities. - Sergio Amat; Zhilin Li 002; Juan Ruiz-Álvarez 001; Concepcion Solano; Juan Carlos Trillo (Math. Comput. Simul., 2023)

The translation operator. Applications to nonlinear reconstruction operators on nonuniform grids. - Sergio Amat; Pedro Ortiz; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (Math. Comput. Simul., 2023)

A new family of means: the generalized weighted power means and applications. - Sergio Amat; Isabel Jiménez; Juan Ruiz 001; Juan Carlos Trillo; Dionisio F. Yáñez (Int. J. Comput. Math., 2023)

Adapting Cubic Hermite Splines to the Presence of Singularities Through Correction Terms. - Sergio Amat; Zhilin Li 002; Juan Ruiz-Álvarez 001; Concepcion Solano; Juan Carlos Trillo (J. Sci. Comput., 2023)

A new B-spline type approximation method for non-smooth functions. - Sergio Amat; David Levin; Juan Ruiz-Álvarez 001; Dionisio F. Yáñez (Appl. Math. Lett., 2023)

Detection, Measurement and Classification of Discontinuities of Signals Captured with Noise. - Sergio Amat; Sonia Busquier; Denys Orieshkin (Axioms, 2024)

Non-linear WENO B-spline based approximation method. - Sergio Amat; David Levin; Juan Ruiz-Álvarez 001; Dionisio F. Yáñez (Numer. Algorithms, 2025)