Related papers: A Block Lanczos with Warm Start Technique for Acce…

The Levenberg-Marquardt (LM) method is commonly used for inverting models used to describe geothermal, groundwater, or oil and gas reservoirs. In previous studies LM parameter updates have been made tractable for highly parameterized…

Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm…

The spectral decomposition of a real skew-symmetric matrix $A$ can be mathematically transformed into a specific structured singular value decomposition (SVD) of $A$. Based on such equivalence, a skew-symmetric Lanczos bidiagonalization…

Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…

While semidefinite programming (SDP) has traditionally been limited to moderate-sized problems, recent algorithms augmented with matrix sketching techniques have enabled solving larger SDPs. However, these methods achieve scalability at the…

The problem of sensor network localization (SNL) can be formulated as a semidefinite programming problem with a rank constraint. We propose a new method for solving such SNL problems. We factorize a semidefinite matrix with the rank…

Computing the null space of a large sparse matrix $A$ is a challenging computational problem, especially if the nullity -- the dimension of the null space -- is not small. When applying a block Lanczos method to $A^\mathsf{T} A$ for this…

The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi…

We propose a thick-restart block Lanczos method, which is an extension of the thick-restart Lanczos method with the block algorithm, as an eigensolver of the large-scale shell-model calculations. This method has two advantages over the…

Deep Neural Networks (DNNs) have demonstrated impressive performance across a wide range of tasks. However, deploying DNNs on edge devices poses significant challenges due to stringent power and computational budgets. An effective solution…

Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension. We introduce the multi-targeted density matrix renormalization group method that acts on a…

We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…

Fast computation of singular value decomposition (SVD) is of great interest in various machine learning tasks. Recently, SVD methods based on randomized linear algebra have shown significant speedup in this regime. This paper attempts to…

In image denoising (IDN) processing, the low-rank property is usually considered as an important image prior. As a convex relaxation approximation of low rank, nuclear norm based algorithms and their variants have attracted significant…

The method of quantum Lanczos recursion is extended to solve for multiple excitations on the quantum computer. While quantum Lanczos recursion is in principle capable of obtaining excitations, the extension to a block Lanczos routine can…

The combination of the variational Monte Carlo (VMC) method with deep learning wave function architectures has led to several successes in ground-state calculations of quantum many-body systems in recent years. However, commonly used…

The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary…

Quadratic minimization problems with orthogonality constraints (QMPO) play an important role in many applications of science and engineering. However, some existing methods may suffer from low accuracy or heavy workload for large-scale…

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a…