Research interests of the Division are related to development of theoretical background of scientific computing and the development and validation of mathematical software developed on these theoretical concepts. Research directions are based on recent activities and results within research projects. Results are applicable in different disciplines.
Scientific interest od chair members is particularly oriented to:
- Matrix spectral decomposition. In addition to development of numerical algorithms, we work on the theory of perturbation and on the convergence proofs. The goal is to continue successful integration of our software into the LAPACK software package.
- Control theory. Activities include both the development of theoretical and numerical aspects, and the application of control theory to concrete engineering problems.
- Reduction of dynamic system dimensions and data-driven methods. We develop methods for identification and approximation of dynamical systems to low-dimension models.
- Operator equations. We work on the development of algebraic methods of approximation of operator equations (Lyapunov and Riccati equations) by a low rank operator approximation, based on the Krylov type, as well as a modern approach based on random sampling in the operator image.
- Spectral analysis of mechanical systems. Development of numerical methods for solving linear and nonlinear eigenvalue problems in different applications.
- Spline approximations. We investigate approximations with a special type of spline function, such as Chebyshev splines, cycloid splines, tension splines, and q-splines. In addition to the development of new numerical algorithms for efficient computing of these splines, the theory of their approximation properties is developed, and based on them, algorithms for specific applications.
- Numerical methods for singularly perturbed problem for ODE. We study application of tension splines to this problem as well as development of exponentially fitted difference schemes of high order.
Members of the Division teach different courses from the field of numerical mathematics on the all levels of our studies.