Description
Chair: Nicola Guglielmi
In this talk we focus on the numerical solution of large-scale symmetric positive definite matrix equations of the form $A_1XB_1^\top + A_2XB_2^\top + \dots + A_\ell X B_\ell^\top = F$, which arise from discretized partial differential equations and control problems. These equations frequently admit low-rank approximations of the solution $X$, particularly when the right-hand side matrix $F$...
We are interested in the numerical solution of the multiterm tensor least squares problem
$$
\min_{\mathcal{X}} \| \mathcal{F} - \sum_{i =0}^{\ell} \mathcal{X} \times_1 A_1^{(i)} \times_2 A_2^{(i)} \cdots \times_d A_d^{(i)} \|_F,
$$
where $\mathcal{X}\in\mathbb{R}^{m_1 \times m_2 \times \cdots \times m_d}$, $\mathcal{F}\in\mathbb{R}^{n_1\times n_2 \times \cdots \times n_d}$ are tensors...
In this work, we present the tree tensor network Nyström (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker or tensor-train formats, to the more general tree tensor network format, enabling a unified treatment of various existing methods. Our method retains the key features of the generalized Nyström approximation for matrices, i.e. it is...
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems, of which the inner one can be solved either exactly or cheaply, while the outer one can be recast as an unconstrained optimization task over a smooth real...
Consider the affine rank minimization problem [6] defined as
\begin{equation}
\begin{aligned}
\min & \quad \text{rank}(X) \
\textrm{s.t.} & \quad \mathcal{C}_\mathcal{A} (X) = b,
\end{aligned}
\tag{1}
\end{equation}
where $X \in \mathbb{R}^{n_1 \times n_2}$ is a matrix, and linear map $\mathcal{C}_\mathcal{A} : \mathbb{R}^{n_1 \times n_2} \rightarrow \mathbb{R}^m$...
