Related papers: Recycling BiCG with an Application to Model Reduct…
Continual learning (CL) studies the problem of learning a sequence of tasks, one at a time, such that the learning of each new task does not lead to the deterioration in performance on the previously seen ones while exploiting previously…
Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…
One of the limitations of recycled GCRO methods is the large amount of computation required to orthogonalize the basis vectors of the newly generated Krylov subspace for the approximate solution when combined with those of the recycle…
The computation of the partial generalized singular value decomposition (GSVD) of large-scale matrix pairs can be approached by means of iterative methods based on expanding subspaces, particularly Krylov subspaces. We consider the joint…
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…
An algorithm for the numerical inversion of large matrices, the biconjugate gradient algorithm (BGA), is investigated in view of its use for Monte Carlo simulations of fermionic field theories. It is compared with the usual conjugate…
Three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…
Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…
Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…
We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the…
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…
We present a new Krylov subspace recycling method for solving a linear system of equations, or a sequence of slowly changing linear systems. Our approach is to reduce the computational overhead of recycling techniques while still benefiting…
Enlarged Krylov subspace methods and their s-step versions were introduced [7] in the aim of reducing communication when solving systems of linear equations Ax = b. These enlarged CG methods consist of enlarging the Krylov subspace by a…
Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly. In PDE constrained shape optimization, these appear naturally, as hundreds or more optimization steps are needed with…
Krylov subspace methods are an essential building block in numerical simulation software. The efficient utilization of modern hardware is a challenging problem in the development of these methods. In this work, we develop Krylov subspace…
Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…
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…
Our goal in this paper is to clarify the relationship between the block Lanczos and the block conjugate gradient (BCG) algorithms. Under the full rank assumption for the block vectors, we show the one-to-one correspondence between the…
Charged particle reconstruction or track reconstruction is one of the most crucial components of pattern recognition in high-energy collider physics. It is known to entail enormous consumption of computing resources, especially when the…