Numerical Linear Algebra
Cluster
- Numerical Analysis
Description
A wide range of mathematical models coming from scientific calculations, engineering, information retrieval and other applications in different fields implies the solution of computational problems that are typical of matrix algebra, such as, in particular, linear equation systems, eigenvalue problems and singular-value problems. Frequently, these computational problems are structured, that is, they feature specific aspects differentiating them from problems of the same type but having their origin in different models; for instance, matrices may feature symmetries, be described by only a few parameters, or be characterised by peculiarities typical of a certain field of application.
Also, practical considerations such as data size, memory usage, calculation time, or the need to achieve accurate and reliable solutions, restrict or prevent the use of classical techniques for the solution of computational problems. The analysis and utilisation of their mathematical structures then becomes the key for identifying efficient solution methods, capable of handling large-sized cases, which could not be tackled otherwise.
The group's research activity includes both the analysis of theoretical and computational properties of structured matrices and the design and analysis of numerical algorithms for the solution of computational problems in which linear algebra techniques intervene.
Research subjects
- Analysis of spectral and computational properties of graph matrices or having special structures
- Synthesis of efficient algorithms for linear numerical algebra problems
ERC panels
- PE1_17 Mathematical aspects of computer science
- PE1_18 Numerical analysis
- PE1_20 Control theory, optimisation and operational research
Tags
- Analisi numerica; algebra lineare numerica; matrici strutturate;
- algoritmi numerici; complessità computazionale.