相关论文: Approximation of sequences of symmetric matrices w…

This paper concerns exact linesearch quasi-Newton methods for minimizing a quadratic function whose Hessian is positive definite. We show that by interpreting the method of conjugate gradients as a particular exact linesearch quasi-Newton…

The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas…

Stochastic gradient descent and other first-order variants, such as Adam and AdaGrad, are commonly used in the field of deep learning due to their computational efficiency and low-storage memory requirements. However, these methods do not…

We present a MATLAB implementation of the symmetric rank-one (SC-SR1) method that solves trust-region. subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix, which can be used for…

We consider the problem of solving linear systems of equations arising with limited-memory members of the restricted Broyden class of updates and the symmetric rank-one (SR1) update. In this paper, we propose a new approach based on a…

In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…

The problem of symmetric rank-one approximation of symmetric tensors is important in Independent Components Analysis, also known as Blind Source Separation, as well as polynomial optimization. We analyze the symmetric rank-one approximation…

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative…

We propose an algorithm that approximates a given matrix polynomial of degree $d$ by another skew-symmetric matrix polynomial of a specified rank and degree at most $d$. The algorithm is built on recent advances in the theory of generic…

Many of today's problems require techniques that involve the solution of arbitrarily large systems $A\mathbf{x}=\mathbf{b}$. A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor…

The problem of low rank approximation is ubiquitous in science. Traditionally this problem is solved in unitary invariant norms such as Frobenius or spectral norm due to existence of efficient methods for building approximations. However,…

In this paper, we investigate the generalized low rank approximation to the symmetric positive semidefinite matrix in the Frobenius norm: $$\underset{ rank(X)\leq k}{\min} \sum^m_{i=1}\left \Vert A_i - B_i XB_i^T \right \Vert^2_F,$$ where…

Low rank approximation has been extensively studied in the past. It is most suitable to reproduce rectangular like structures in the data. In this work we introduce a generalization using shifted rank-1 matrices to approximate…

The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Many matrices appearing in numerical methods for partial differential equations and integral equations are rank-structured, i.e., they contain submatrices that can be approximated by matrices of low rank. A relatively general class of…

Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…