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In tensor completion, the goal is to fill in missing entries of a partially known tensor under a low-rank constraint. We propose a new algorithm that performs Riemannian optimization techniques onâ€¦ (More)

An entry of X is denoted by Xi1,...,id where each index iÎ¼ âˆˆ {1, . . . , nÎ¼} refers to the Î¼th mode of the tensor for Î¼ = 1, . . . , d. For simplicity, we will assume that X has real entries, but itâ€¦ (More)

- Daniel Kressner
- Numerische Mathematik
- 2009

We consider matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. One of the most fundamental differences to the linear case is that distinct eigenvalues may have linearlyâ€¦ (More)

- Daniel Kressner, Christine Tobler
- SIAM J. Matrix Analysis Applications
- 2011

Abstract. We consider linear systems A(Î±)x(Î±) = b(Î±) depending on possibly many parameters Î± = (Î±1, . . . , Î±p). Solving these systems simultaneously for a standard discretization of the parameterâ€¦ (More)

- Daniel Kressner, Christine Tobler
- ACM Trans. Math. Softw.
- 2012

The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. This article presents a Matlab toolbox, along with the underlying methodologyâ€¦ (More)

- Bo KÃ¥gstrÃ¶m, Daniel Kressner
- SIAM J. Matrix Analysis Applications
- 2006

Abstract. New variants of the QZ algorithm for solving the generalized eigenvalue problem are proposed. An extension of the small-bulge multishift QR algorithm is developed, which chases chains ofâ€¦ (More)

- Daniel Kressner
- 2004

- Daniel Kressner, Christine Tobler
- Comput. Meth. in Appl. Math.
- 2011

We consider elliptic PDE eigenvalue problems on a tensorized domain, discretized such that the resulting matrix eigenvalue problem Ax Î»x exhibits Kronecker product structure. In particular, we areâ€¦ (More)

- Daniel Kressner, MarÃa JosÃ© PelÃ¡ez, Julio Moro
- SIAM J. Matrix Analysis Applications
- 2009

The sensitivity of a multiple eigenvalue of a matrix under perturbations can be measured by its HÃ¶lder condition number. Various extensions of this concept are considered. A meaningful notion ofâ€¦ (More)

- Peter Benner, Daniel Kressner
- ACM Trans. Math. Softw.
- 2006

This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonalâ€¦ (More)