Related papers: Multigrid methods for block-Toeplitz linear system…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a previous paper, the authors have developed an analysis for the first biharmonic…
Multi-block grids provide the computational efficiency of structured grids and the flexibility for complex geometry. Thus, Multi-block structured grids are widely used for field simulation on complex domains. In this paper we propose a…
A fast algorithm for the large-scale joint inversion of gravity and magnetic data is developed. It uses a nonlinear Gramian constraint to impose correlation between density and susceptibility of reconstructed models. The global objective…
Solving the Toeplitz systems, which is to find the vector $x$ such that $T_nx = b$ given an $n\times n$ Toeplitz matrix $T_n$ and a vector $b$, has a variety of applications in mathematics and engineering. In this paper, we present a…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
Motivated by robust matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss function applied to the sum of two blocks of variables,…
Superregular matrices have the property that all of their submatrices, which can be full rank are so. Lower triangular superregular matrices are useful for e.g., maximum distance separable convolutional codes as well as for (sequential)…
Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with…
Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for…
The solution of parameter-dependent linear systems, by classical methods, leads to an arithmetic effort that grows exponentially in the number of parameters. This renders the multigrid method, which has a well understood convergence theory,…
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space $H^2_{\mathbb{C}^n}$ of the unit circle. Firstly, we establish a tractable and explicit criterion on the…
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…
In this paper, we consider the problem of seriation of a permuted structured matrix based on noisy observations. The entries of the matrix relate to an expected quantification of interaction between two objects: the higher the value, the…
This paper studies two structured approximation problems: (1) Recovering a corrupted low-rank Toeplitz matrix and (2) recovering the range of a Fourier matrix from a single observation. Both problems are computationally challenging because…
In this paper we analyse the convergence properties of two-level, W-cycle and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear system of equations stemming from the lowest order…
We study the convergence of multigrid schemes for the Helmholtz equation, focusing in particular on the choice of the coarse scale operators. Let G_c denote the number of points per wavelength at the coarse level. If the coarse scale…