6 citations · 7 across the 6 of their papers we have counts for
7 papers
A single LU~factorization approach to model reduction for linear system families with a quadratic matrix pencil
Mikhail A. Botchev, Leonid Knizhnerman, Nikolai L. Zamarashkin +1
To solve a family of large linear systems where the system matrix depends on the family parameter quadratically, we propose a new solution approach. Our method employs the derivati…
Rational Hermite-Padé Approximants vs Padé Approximants. Numerical Results
Egor O. Dobrolyubov, Nikolay R. Ikonomov, Leonid A. Knizhnerman +1
The main purpose of the paper is to present some powerful data on the advantage of the rational approximation procedure based on Hermite-Padé polynomials over the Padé approximatio…
Krylov subspace residual and restarting for certain second order differential equations
M. A. Botchev, L. A. Knizhnerman, M. Schweitzer
We propose algorithms for efficient time integration of large systems of oscillatory second order ordinary differential equations (ODEs) whose solution can be expressed in terms of…
Model order reduction of layered waveguides via rational Krylov fitting
Vladimir Druskin, Stefan Güttel, Leonid Knizhnerman
Rational approximation recently emerged as an efficient numerical tool for the solution of exterior wave propagation problems. Currently, this technique is limited to wave media wh…
A residual concept for Krylov subspace evaluation of the matrix function
Mike A. Botchev, Leonid A. Knizhnerman, Eugene E. Tyrtyshnikov
An efficient Krylov subspace algorithm for computing actions of the matrix function for large matrices is proposed. This matrix function is widely used in exponential time inte…
ART: adaptive residual--time restarting for Krylov subspace matrix exponential evaluations
Mikhail A. Botchev, Leonid A. Knizhnerman
In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some converge…
Near-optimal perfectly matched layers for indefinite Helmholtz problems
Vladimir Druskin, Stefan Güttel, Leonid Knizhnerman
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rationa…