Related papers: Flexible Krylov Methods for Group Sparsity Regular…
The Riesz maps of the $L^2$ de Rham complex frequently arise as subproblems in the construction of fast preconditioners for more complicated problems. In this work we present multigrid solvers for high-order finite element discretizations…
In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…
The resolvent Krylov subspace method builds approximations to operator functions $f(A)$ times a vector $v$. For the semigroup and related operator functions, this method is proved to possess the favorable property that the convergence is…
The sparse group lasso is a high-dimensional regression technique that is useful for problems whose predictors have a naturally grouped structure and where sparsity is encouraged at both the group and individual predictor level. In this…
Reconstructing high-quality images with sharp edges requires the use of edge-preserving constraints in the regularized form of the inverse problem. The use of the $\ell_q$-norm on the gradient of the image is a common such constraint. For…
Subspace clustering refers to the problem of clustering high-dimensional data that lie in a union of low-dimensional subspaces. State-of-the-art subspace clustering methods are based on the idea of expressing each data point as a linear…
A primary computational problem in kernel regression is solution of a dense linear system with the $N\times N$ kernel matrix. Because a direct solution has an O($N^3$) cost, iterative Krylov methods are often used with fast matrix-vector…
Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the…
This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial guesses over a sequence of linear systems with…
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the…
Conjugated gradients on the normal equation (CGNE) is a popular method to regularise linear inverse problems. The idea of the method can be summarised as minimising the residuum over a suitable Krylov subspace. It is shown that using the…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…
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…
We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse regularization techniques that are based on frame representations, we train an encoder-decoder network by including an $\ell^1$-penalty.…