INTEC researcher co-leads development of optimal iterative method for systems of nonlinear equations
INTEC highlights the contribution of Dr. María Penkova Vassileva to the development of an optimal-order iterative scheme for solving nonlinear systems, published in a high-impact journal, with applications in engineering and scientific computing. The research is being announced in the context of the International Day of Women in Mathematics.
SANTO DOMINGO – The Instituto Tecnológico de Santo Domingo (INTEC) presents the results of an international research project led by Dr. Maria Penkova Vassileva, director of the Doctoral Program in Mathematics at the institution, which has culminated in the development of an optimal fourth-order iterative method for solving systems of nonlinear equations, within the framework of a collaborative network with the Universitat Politècnica de València (Spain) and other Dominican universities
The research, titled "Generalized Traub Family for Solving Nonlinear Systems: Fourth-Order Optimal Method and Dynamic Analysis," was published in the scientific journal Mathematics. The work introduces the Generalized Traub Method (GTM), a tool designed to solve systems of nonlinear equations with greater stability than models commonly used in engineering and physics.
Fourth-order optimization
The significance of this finding lies in its classification as "optimal." In numerical analysis, a method is considered optimal when it achieves the highest possible order of convergence using the minimum computational resources. The scheme developed by Penkova and her international team addresses the Cordero-Torregrosa Conjecture, allowing the solution of systems with up to 1,000 variables with high precision and reduced operating costs.
This advancement has direct applications in optimizing complex technological processes. According to the technical text, the GTM method offers a balance between accuracy and stability, critical factors for systems requiring repetitive calculations, such as the positioning of artificial satellites or the training of artificial intelligence models that process large volumes of data.
The project is the result of a scientific collaboration network between INTEC and the Polytechnic University of Valencia (Spain), with the participation of researchers from the Autonomous University of Santo Domingo, APEC University, and the Salomé Ureña Higher Institute of Teacher Training. This alliance links Dominican academia with European research centers.
About Dr. Penkova and the PhD in Mathematics
Dr. Penkova Vassileva is a researcher in numerical analysis and nonlinear systems. She currently directs the PhD program in Mathematics at INTEC, a program focused on training specialists for technological and scientific innovation in the Dominican Republic.
The doctoral program, which is being developed in coordination with three local universities and the Ministry of Higher Education, Science and Technology (Mescyt), seeks to strengthen mathematical research in the country to support national competitiveness and promote the exchange of knowledge with international experts.
International Day of Women Mathematics
International Women in Mathematics Day is celebrated every May 12 to commemorate the birth of Maryam Mirzakhani, the first woman to win the Fields Medal, an international award for outstanding discoveries in mathematics. This day aims to highlight female talent in this discipline, break down gender barriers, and inspire future generations.