相关论文: The joint bidiagonalization method for large GSVD …

The generalized singular value decomposition (GSVD) is a powerful tool for solving discrete ill-posed problems. In this paper, we propose a two-sided uniformly randomized GSVD algorithm for solving the large-scale discrete ill-posed problem…

A combination $\mathbf{a}+\mathrm{i}\mathbf{b}$ where ${\mathrm i}^2=-1$ and $\mathbf{a}, \, \mathbf{b}$ are real vectors is called a bivector. Gibbs developed a theory of bivectors, in which he associated an ellipse with each bivector. He…

The Lanczos method is one of the most powerful and fundamental techniques for solving an extremal symmetric eigenvalue problem. Convergence-based error estimates depend heavily on the eigenvalue gap. In practice, this gap is often…

We present a generalisation of the pseudoinverse operation to pairs of matrices, as opposed to single matrices alone. We note the fact that the Singular Value Decomposition can be used to compute the ordinary Moore-Penrose pseudoinverse. We…

We solve the Hubbard model with the exact diagonalization method on a graphics processing unit (GPU). We benchmark our GPU program against a sequential CPU code by using the Lanczos algorithm to solve the ground state energy in two cases: a…

This paper is concerned with partial Joint SVD-type Block Diagonalization of several matrices so that the extracted diagonal parts collectively optimally assume part of the total mass of all given matrices. For that reason, it will be…

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential…

Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two…

The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…

Singular Value Decomposition (SVD) is the basic body of many statistical algorithms and few users question whether SVD is properly handling its job. SVD aims at evaluating the decomposition that best approximates a data matrix, given some…

Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The performance of such techniques has been extensively…

We demonstrate a novel technique to obtain singular-value decomposition (SVD) of the coupled-cluster triple excitations amplitudes, $t_{ijk}^{abc}$. The presented method is based on the Golub-Kahan bidiagonalisation strategy and does not…

Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…

In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…

Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a…

We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…

In this paper, we propose a two-level block preconditioned Jacobi-Davidson (BPJD) method for efficiently solving discrete eigenvalue problems resulting from finite element approximations of $2m$th ($m = 1, 2$) order symmetric elliptic…

The randomized singular value decomposition (R-SVD) is a popular sketching-based algorithm for efficiently computing the partial SVD of a large matrix. When the matrix is low-rank, the R-SVD produces its partial SVD exactly; but when the…

This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the…