Rate My Professor José Manuel Gutiérrez

José Manuel Gutiérrez is a leading expert in applied mathematics, particularly in the development and analysis of iterative methods for solving nonlinear equations. He earned his PhD in Mathematical Sciences from the Universidad de La Laguna in 1995, with a thesis titled 'El método de Newton en espacios de Banach,' supervised by Dr. Miguel Ángel Hernández Verón. His academic career at the University of La Rioja began in 1998 as Profesor Titular de Universidad in the Department of Mathematics and Computation, where he progressed to Catedrático de Universidad in 2022. Gutiérrez participates in the doctoral program in Mathematics and Computation and is a member of research groups including PRIENOL (Grupo de Procesos Iterativos y Ecuaciones no Lineales), Model3DBio Bioinformática Estructural, Modelado y Mecanismos Biológicos. His research interests encompass convergence analysis of iterative processes, dynamical behavior of iterative schemes, and numerical resolution of nonlinear equations across various domains, from real and complex numbers to Banach spaces.

Gutiérrez has made substantial contributions through numerous publications in prestigious journals. Key works include 'Geometric constructions of iterative functions to solve nonlinear equations' (2003, 421 citations), 'A family of Chebyshev-Halley type methods in Banach spaces' (1997, 371 citations), 'An acceleration of Newton's method: Super-Halley method' (2001, 255 citations), 'Recurrence relations for the super-Halley method' (1998, 204 citations), and more recent papers such as 'A Graphic Method for Detecting Multiple Roots Based on Self-Maps of the Hopf Fibration and Nullity Tolerances' (Mathematics, 2021), 'A Characterization of the Dynamics of Schröder's Method for Polynomials with Two Roots' (Fractal and Fractional, 2021), 'Extending the applicability of Newton's method for a class of boundary value problems using the shooting method' (Applied Mathematics and Computation, 2020), and 'Superattracting extraneous fixed points and n-cycles for Chebyshev's method on cubic polynomials' (Qualitative Theory of Dynamical Systems, 2020). He has authored around 15 research articles in recent years and co-edited 'Notas de Ecuaciones en Derivadas Parciales' (2021). His influential research has advanced efficient numerical algorithms, impacting fields like computational mathematics.