香蕉视频

Vladimir Druskin
Schlumberger-Doll Research Center

Krylov subspace approach (e.g., the conjugate gradients) is the method of choice for the iterative solutions of large linear systems of algebraic equations. In 1980's it emerged as an algorithm for systems of linear differential equations arisen from the semidiscretization of evolutionary PDEs. When applicable it exhibits dramatic advantage compared to the conventional time-stepping methods. More recently the Krylov subspace projection became the main tool for the construction of reduced order models for large scale linear time-invariant dynamical systems. We will guide through main algorithmic details and analysis of the approach, then discuss its generalizations such as the Rational Krylov Subspace Reduction and the Parameter-Dependent Krylov Subspace Reduction (a.k.a. interpolatory projection) and also connection to some classical results from the approximation theory. The talk will be illustrated with numerical examples from electromagnetic oil exploration.