Related papers: Structural properties of Krylov subspaces, Krylov …
We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace resp. Heisenberg subgroup. These operators are shown to be…
The article deals with iterative methods of solving linear operator equations $x = Bx + f$ and $Ax = f$ with self-adjoint operators in Hilbert space $X$ in critical case when $\rho(B) = 1$ and $0 \in {\rm Sp}\, A$. The main results are…
Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and…
This is a companion to recent papers of the authors; here we construct the `noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the…
We prove uniform boundedness of certain boundary representations on appropriate fractional Sobolev spaces $W^{s,p}$ with $p>1$ for arbitrary Gromov hyperbolic groups. These are closed subspaces of $L^p$ and in particular Hilbert spaces in…
In this paper we solve the problem of approximating functionals $(\varphi(A)x, f)$ (where $\varphi(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another…
Interior point methods are widely used for different types of mathematical optimization problems. Many implementations of interior point methods in use today rely on direct linear solvers to solve systems of equations in each iteration. The…
The Krylov subspace projection approach is a well-established tool for the reduced order modeling of dynamical systems in the time domain. In this paper, we address the main issues obstructing the application of this powerful approach to…
Krylov complexity provides a powerful framework for characterizing the dynamical evolution of quantum systems through the spreading of states in Krylov space. The motivation for this is rooted in the optimality of the Krylov basis for the…
We provide convergence rates for Krylov subspace solutions to the trust-region and cubic-regularized (nonconvex) quadratic problems. Such solutions may be efficiently computed by the Lanczos method and have long been used in practice. We…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
An algorithm for constructing a $J$-orthogonal basis of the extended Krylov subspace $\mathcal{K}_{r,s}=\operatorname{range}\{u,Hu, H^2u,$ $ \ldots, $ $H^{2r-1}u, H^{-1}u, H^{-2}u, \ldots, H^{-2s}u\},$ where $H \in \mathbb{R}^{2n \times…
We revise the strong convergent Chernoff product formula and extend it, in a Hilbert space, to convergence in the operator-norm topology. Main results deal with the self-adjoint Chernoff product formula. The nonself-adjoint case concerns…
The solution of linear inverse problems when the unknown parameters outnumber data requires addressing the problem of a nontrivial null space. After restating the problem within the Bayesian framework, a priori information about the unknown…
We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures for diagonally dominant $J$-self-adjoint operator matrices. These are used in the proof of the central result, a perturbation…
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…
Motivated by bulk reconstruction of smeared boundary operators, we study the Krylov complexity of local and non-local primary CFT$_d$ operators from the local bulk-to-bulk propagator of a minimally-coupled massive scalar field in…
The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-self-adjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that…
The Kruglov property and the Kruglov operator play an important role in the study of geometric properties of r.i. function spaces. We prove that the boundedness of the Kruglov operator in a r.i. space is equivalent to the uniform…