18 citations · 36 across the 13 of their papers we have counts for
15 papers
Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems
Stefano Giani, Luka Grubišić, Luca Heltai +1
We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigen…
A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques
Stefano Giani, Luka Grubisic, Harri Hakula +1
We propose an a posteriori error estimator for high-order - or -finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for est…
Stochastic collocation method for computing eigenspaces of parameter-dependent operators
Luka Grubišić, Harri Hakula, Mikael Laaksonen
We consider computing eigenspaces of an elliptic self-adjoint operator depending on a countable number of parameters in an affine fashion. The eigenspaces of interest are assumed t…
Analysis of FEAST spectral approximations using the DPG discretization
Jay Gopalakrishnan, Luka Grubišić, Jeffrey Ovall +1
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as "FEAST", has gained considerable attention in recent years. This work…
Modeling and discretization methods for the numerical simulation of elastic stents
Luka Grubisic, Matko Ljulj, Volker Mehrmann +1
A new model description for the numerical simulation of elastic stents is proposed. Based on the new formulation an inf-sup inequality for the finite element discretization is prov…
Spectral discretization errors in filtered subspace iteration
Jay Gopalakrishnan, Luka Grubišić, Jeffrey Ovall
We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space…
The Tan -Theorem in Fluid Dynamics
Luka Grubišić, Vadim Kostrykin, Konstantin A. Makarov +2
We show that the generalized Reynolds number (in fluid dynamics) introduced by Ladyzhenskaya is closely related to the rotation of the positive spectral subspace of the Stokes bloc…
Reliable a-posteriori error estimators for -adaptive finite element approximations of eigenvalue/eigenvector problems
Stefano Giani, Luka Grubišić, Jeffrey Ovall
We present reliable a-posteriori error estimates for -adaptive finite element approximations of eigenvalue/eigenvector problems. Starting from our earlier work on adaptive…
The Rotation of Eigenspaces of Perturbed Matrix Pairs
Luka Grubišić, Ninoslav Truhar, Krešimir Veselić
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent…
The TAN Theorem for Indefinite Quadratic Forms
Luka Grubišić, Vadim Kostrykin, Konstantin A. Makarov +1
A version of the Davis-Kahan Tan theorem [SIAM J. Numer. Anal. \textbf{7} (1970), 1 -- 46] for not necessarily semibounded linear operators defined by quadratic forms is prove…
Representation Theorems for Indefinite Quadratic Forms Revisited
Luka Grubisic, Vadim Kostrykin, Konstantin A. Makarov +1
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given…
Relative convergence estimates for the spectral asymptotic in the Large Coupling Limit
Luka Grubisic
We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our profs are constructive in nature and use (elementary) t…
On Temple--Kato like inequalities and applications
Luka Grubisic
We give both lower and upper estimates for eigenvalues of unbounded positive definite operators in an arbitrary Hilbert space. We show scaling robust relative eigenvalue estimates…
On weakly formulated Sylvester equations and applications
Luka Grubisic, Kresimir Veselic
We use a ``weakly formulated'' Sylvester equation to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint o…
On eigenvalue and eigenvector estimates for nonnegative definite operators
Luka Grubisic
In this article we further develop a perturbation approach to the Rayleigh--Ritz approximations from our earlier work. We both sharpen the estimates and extend the applicability of…