相关论文: Two iterative formulas of largest and smallest sin…
We give a formula for the inverse matrix to an infinite matrix with possibly noncommutative entries, generalizing the Newton interpolation formula and the Taylor formula.
A counter-example to lower bounds for the singular values of the sum of two matrices in [1] and [2] is given. Correct forms of the bounds are pointed out.
Square matrices of the form $\widetilde{\mathbf{A}} =\mathbf{A} + \mathbf{e}D \mathbf{f}^*$ are considered. An explicit expression for the inverse is given, provided $\widetilde{\mathbf{A}}$ and $D$ are invertible with…
It is known that singular values of idempotent matrices are either zero or larger or equal to one \cite{HouC63}. We state exactly how many singular values greater than one, equal to one, and equal to zero there are. Moreover, we derive a…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
A discrete map based on the sum of an integer's distinct primes factors and the sum of its other factors is defined and its iteration is studied.
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
Iterative equation is an equality with an unknown function and its iterates. There were not found a result on iterative equations with multiplication of iterates of the unknown function on $\mathbb{R}$. In this paper we use an exponential…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed dimensions. For an N by n matrix A with independent and identically distributed subgaussian entries, the smallest singular value…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
We prove an estimate on the smallest singular value of a multiplicatively and additively deformed random rectangular matrix. Suppose $n\le N \le M \le \Lambda N$ for some constant $\Lambda \ge 1$. Let $X$ be an $M\times n$ random matrix…
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…
In Communication theory and Coding, it is expected that certain circulant matrices having $k$ ones and $k+1$ zeros in the first row are nonsingular. We prove that such matrices are always nonsingular when $2k+1$ is either a power of a…
To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence. These maps are based on model functions which can be written as an inner product. The main family of maps discussed is…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…