Square matrix

About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.

Global Positioning System Integer Ambiguity Resolution Using Factorized Least-Squares Techniques

Abstract: Factorized methods are developed for rapid solution of integer least-squares problems that arise when resolving Global Positioning System carrier cycle ambiguities. Such algorithms can enhance batch estimators and Kalman filters that use carrier-phase differential Global Positioning System data for relative spacecraft position estimation or for attitude determination. The solution of mixed real/integer linear least-squares problems is reviewed, and new algorithms are developed to speed the solution of the integer part of such problems. One new algorithm generates a candidate set of integer vectors that is bounded by an ellipsoid and that is guaranteed to contain the solution. Once generated, this set is searched by brute force to find the integer optimum. The set generator is based on the principle of backsubstitution for upper-triangular linear systems. Two new preconditioning algorithms are developed based on a principle of least-squares ambiguity decorrelation adjustment that seeks an increasing order in the magnitudes of the diagonal elements of the problem's upper-triangular square-root information matrix. These new algorithms decrease computation times in comparison to their nearest competitors by factors ranging from 2 to 4 for a random set of problems that have between 11 and 50 integer unknowns.

Error Estimates for Polynomial Krylov Approximations to Matrix Functions

Abstract: In this paper we are interested in the polynomial Krylov approximations for the computation of $\varphi(A)v$, where $A$ is a square matrix, $v$ represents a given vector, and $\varphi$ is a suitable function which can be employed in modern integrators for differential problems. Our aim consists of proposing and analyzing innovative a posteriori error estimates which allow a good control of the approximation procedure. The effectiveness of the results we provide is tested on some numerical examples of interest.

An Adaptive Correction Approach for Tensor Completion

Abstract: In this paper, we study the tensor completion problem on recovery of the multilinear data under limited sampling. A popular convex relaxation of this problem is to minimize the nuclear norm of the more square matrix produced by matricizing a tensor. However, it may fail to produce a highly accurate solution under low sample ratio. In order to get a recovery with high accuracy, we propose an adaptive correction approach for tensor completion. First, a corrected model for matrix completion with bound constraint is proposed and its error bound is established. Then, we extend it to tensor completion with bound constraint and propose a corrected model for tensor completion. The adaptive correction approach consists of solving a series of corrected models with an initial estimator where the initial estimator used for the next step is computed from the value of the current solution. Moreover, the error bound of the corrected model for tensor completion is also established. A convergent 3-block alternating direct...