相关论文: On computing the symplectic $LL^T$ factorization

In this paper, we consider two fundamental symmetric kernels in linear algebra: the Cholesky factorization and the symmetric rank-$k$ update (SYRK), with the classical three nested loops algorithms for these kernels. In addition, we…

A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an…

This paper uses matrix transformations to provide the Autoone-Takagi decomposition of dual complex symmetric matrices and extends it to dual quaternion $\eta$-Hermitian matrices. The LU decomposition of dual matrices is given using the…

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…

Sparse linear algebra routines are fundamental building blocks of a large variety of scientific applications. Direct solvers, which are methods for solving linear systems via the factorization of matrices into products of triangular…

Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…

This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$. Instead of computing the R factor from $X^T X$, as is done by standard methods, we obtain it from a small, efficiently…

We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…

We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…

Tile low rank representations of dense matrices partition them into blocks of roughly uniform size, where each off-diagonal tile is compressed and stored as its own low rank factorization. They offer an attractive representation for many…

Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case).…

Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

Our interest lies in the robust and efficient solution of large sparse linear least-squares problems. In recent years, hardware developments have led to a surge in interest in exploiting mixed precision arithmetic within numerical linear…

Local Fourier analysis is a strong and well-established tool for analyzing the convergence of numerical methods for partial differential equations. The key idea of local Fourier analysis is to represent the occurring functions in terms of a…

We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…

This paper develops and analyzes a new algorithm for QR decomposition with column pivoting (QRCP) of rectangular matrices with many more rows than columns. The algorithm carefully combines methods from randomized numerical linear algebra to…

For every $2n\times 2n$ real positive definite matrix $A,$ there exists a real symplectic matrix $M$ such that $M^TAM=\diag(D,D),$ where $D$ is the $n\times n$ positive diagonal matrix with diagonal entries $d_1(A)\le \cdots\le d_n(A).$ The…

Computing Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to…

In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical…