Computational linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers. It is often a fundamental part of engineering and computational science problems, such as image and signal processing, telecommunication, computational finance, materials science simulations, structural biology, data mining, and bioinformatics, fluid dynamics, and many other areas. Such software relies heavily on the development, analysis, and implementation of state-of-the-art algorithms for solving various numerical linear algebra problems, in large part because of the role of matrices in finite difference and finite element methods.

Common problems in numerical linear algebra include computing the following: LU decomposition, QR decomposition, Singular value decomposition, eigenvalues.

As being established in 2011, in the Institute of Informatics the Computational Linear Algebra group has been working actively under the Computational Science and Engineering Graduate programme with a strong support of computer infrastructure. The group heavily concentrates on the multigrid methods, scalable parallel algorithms for linear systems and preconditioners.

Research Topics

• Designing Scalable Algorithms for Large Scale Linear Set of Equations
• Scalable Linear Sparse Solvers for Many-core Distributed Systems
• Scalable Linear Sparse Solvers for Heterogenous Systems
• Nonlinear Algebra: Large Scale Nonlinear Equations
• Large Scale Unconstraint optimization
• Thrust Region (Levenberg-Marquardt) and Line Search Methods
• Quasi-Newton (Inexact Newton Methods)
• Barzilai & Borwein (BB) Like Methods
• BFGS like Quasi-Newton Methods
• Powel Symmetric Broyden (PSB) and Symmeric Rank one (SR1) Methods
• Hybrid Nonlinear Solvers
• Hybrid (Direct and Iterative) Sparse Linear Solvers