Related papers: An improved Krylov eigenvalue strategy using the F…
We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…
Low-precision computing is essential for efficiently utilizing memory bandwidth and computing cores. While many mixed-precision algorithms have been developed for iterative sparse linear solvers, effectively leveraging half-precision (fp16)…
A local and parallel algorithm based on the multilevel discretization is proposed in this paper to solve the eigenvalue problem by the finite element method. With this new scheme, solving the eigenvalue problem in the finest grid is…
Recently, single-frame infrared small target (SIRST) detection technology has attracted widespread attention. Different from most existing deep learning-based methods that focus on improving network architectures, we propose a…
This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of…
We present a novel Krylov subspace method for approximating $L_f(A, E) \vc{b}$, the matrix-vector product of the Fr\'echet derivative $L_f(A, E)$ of a large-scale matrix function $f(A)$ in direction $E$, a task that arises naturally in the…
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace…
Krylov subspace methods are a ubiquitous tool for computing near-optimal rank $k$ approximations of large matrices. While "large block" Krylov methods with block size at least $k$ give the best known theoretical guarantees, block size one…
In this paper, a new type of multi-level correction scheme is proposed for solving eigenvalue problems by finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which…
We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh-Schr\"odinger perturbation theory and termed Iterative Perturbative Theory (IPT). Contrary to standard eigenvalue algorithms, which are either…
Iterative feature space optimization involves systematically evaluating and adjusting the feature space to improve downstream task performance. However, existing works suffer from three key limitations:1) overlooking differences among data…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
The FLAME methodology makes it possible to derive provably correct algorithms from a formal description of a linear algebra problem. So far, the methodology has been successfully used to automate the derivation of direct algorithms such as…
In this paper, we propose an efficient numerical scheme for solving some large scale ill-posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited.…
Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties which are pertinent to the entire sequence, and not just to the single problem. When such features take…
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…
Euclidean Signed Distance Field (ESDF) is useful for online motion planning of aerial robots since it can easily query the distance and gradient information against obstacles. Fast incrementally built ESDF map is the bottleneck for…
We analyze a modified version of Nesterov accelerated gradient algorithm, which applies to affine fixed point problems with non self-adjoint matrices, such as the ones appearing in the theory of Markov decision processes with discounted or…
Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…
The parallel full approximation scheme in space and time (PFASST) is a parallel-in-time integrator that allows to integrate multiple time-steps simultaneously. It has been shown to extend scaling limits of spatial parallelization strategies…