An Algorithm for Approximating Implicit Functions by Polynomials without Higher-Order Differentiability

Thời gian: 14:30 đến 15:30 Ngày 24/11/2023

Địa điểm: Phòng C101, VIASM, 157 phố Chùa Láng, Hà Nội

Tóm tắt:

Speaker 1. Prof. Kyung Soo Rim (14h30-15h30)

Department of Mathematics, Sogang University

Title: An Algorithm for Approximating Implicit Functions by Polynomials without Higher-Order Differentiability

Abstract: We consider an equation of multiple variables in which a partial derivative does not vanish at a point. The implicit function theorem provides a local existence and uniqueness of the function for the equation. In this paper, we propose an algorithm to approximate the function by a polynomial without using higher-order differentiability, which depends essentially on integrability. Moreover, we extend the method to a system of equations if the Jacobian determinant does not vanish. This is a robust method for implicit functions that are not differentiable to higher-order. Additionally, we present two numerical experiments to verify the theoretical results.

Speaker 2. Assoc. Prof. Le Chi Ngoc (15h30-16h30)

School of Applied Mathematics and Informatics, Hanoi University of Science and Technology

Title: Mathematical Modelling and Machine Learning Methods for Environment and Climate Change Issues

Abstract: In this talk, we will present Mathematical Modelling and Machine Learning Methods for Environment and Climate Change issues.