Related papers: New error bounds for linear complementarity proble…

A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in [C.Q. Li et al., A new error bound for linear complementarity problems for B-matrices.…

A new error bound for the linear complementarity problem is given when the involved matrix is a B-matrix. It is shown that this bound is sharper than some previous bounds [C.Q. Li, Y.T. Li. Note on error bounds for linear complementarity…

We focus on the estimating problem of the infinity norm of the inverse of Nekrasov matrices, give new bounds which involve a parameter, and then determine the optimal value of the parameter such that the new bounds are better than those in…

For many applications, it is convenient to have good upper bounds for the norm of the inverse of a given matrix. In this paper, we obtain such bounds when A is a Nekrasov matrix, by means of a scaling matrix transforming A into a strictly…

Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…

In this article we establish error bound for linear complementarity problem with $P$-matrix using plus function. We introduce a fundamental quantity associated with a $P$-matrix and show how this quantity is useful in deriving error bounds…

Absolute value equations, due to their relation to the linear complementarity problem, have been intensively studied recently. In this paper, we present error bounds for absolute value equations. Along with the error bounds, we introduce an…

Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…

Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…

We obtain an expression for the error in the approximation of $f(A) \boldsymbol{b}$ and $\boldsymbol{b}^T f(A) \boldsymbol{b}$ with rational Krylov methods, where $A$ is a symmetric matrix, $\boldsymbol{b}$ is a vector and the function $f$…

We propose a new error bound for the solution of tensor complementarity problem TCP$(q, \mathcal{A})$ given that $\mathcal{A}$ is a $P$-tensor and $q$ is a real vector. We show that the proposed error bound is sharper than the earlier…

In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we…

In this note, we prove that the problem of computing the linear discrepancy of a given matrix is $\Pi_2$-hard, even to approximate within $9/8 - \epsilon$ factor for any $\epsilon > 0$. This strengthens the NP-hardness result of Li and…

In this paper, we introduce semi-infinite tensor complementarity problem to provide an approach for considering a more realistic situation of the problem. We prove the necessary and sufficient conditions for the existence of the solution…

In this paper we establish some new bounds for the companion of Ostrowski's inequality for the case when $f'\in L^1[a,b]$, $f"\in L^2[a,b]$ and $f'\in L^2[a,b]$, respectively. We point out that the results in the first and third cases are…

From the application point of view, it is important to have a good upper bound for the maximum norm of the inverse of a given matrix A. In this paper we will give two simple and practical upper bounds for the maximum norm of the inverse of…

In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

In this paper, by making use of this fact that for $a_{j}, b_{j}\in \mathbb{R}$, $j=1,2,\ldots,n$, there are $\lambda_{j}\in [0,1]$ with $\sum_{j=1}^{n}\lambda_{j}=1$ such that \[ \min_{1\leq j\leq n}\{a_{j}\}-\min_{1\leq j\leq…

To our knowledge, the error and perturbation bounds of the general absolute value equations are not discussed. In order to fill in this study gap, in this paper, by introducing a class of absolute value functions, we study the error and…