Related papers: Bootstrapped Block Lanczos for large-dimension eig…
In this paper, we develop RLOBPCG, an efficient method for computing a small number of singular triplets corresponding to the smallest singular values of large, tall matrices. The algorithm combines randomized preconditioner from the…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…
Block encodings are a fundamental primitive in quantum algorithms, but can often have large ancilla overhead. In this work, we introduce novel techniques for reducing this overhead in two distinct ways. In Part I, we prove the existence of…
Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace--Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The…
Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since…
Randomized sampling has recently been proven a highly efficient technique for computing approximate factorizations of matrices that have low numerical rank. This paper describes an extension of such techniques to a wider class of matrices…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
The computation of a few singular triplets of large, sparse matrices is a challenging task, especially when the smallest magnitude singular values are needed in high accuracy. Most recent efforts try to address this problem through…
Many learning tasks, such as cross-validation, parameter search, or leave-one-out analysis, involve multiple instances of similar problems, each instance sharing a large part of learning data with the others. We introduce a robust framework…
Global and block Krylov subspace methods are efficient iterative solvers for large sparse linear systems with multiple right-hand sides. However, global or block Lanczos-type solvers often exhibit large oscillations in the residual norms…
We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be…
Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is…
The solution of large, sparse constrained least-squares problems is a staple in scientific and engineering applications. However, currently available codes for such problems are proprietary or based on MATLAB. We announce a freely available…
Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present…
We present an efficient approach to simulate real-time quantum dynamics using Projected Variational Quantum Dynamics (PVQD), where the computational cost is reduced by strategically optimizing only a subset of the variational parameters at…
This paper develops column partition based distributed schemes for a class of large-scale convex sparse optimization problems, e.g., basis pursuit (BP), LASSO, basis pursuit denosing (BPDN), and their extensions, e.g., fused LASSO. We are…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Block coordinate descent (BCD) methods are prevalent in large scale optimization problems due to the low memory and computational costs per iteration, the predisposition to parallelization, and the ability to exploit the structure of the…
Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower…