Exponential Least Squares Solvers for Linear Equations over Networks

Exponential Least Squares Solvers for Linear Equations Over Networks

We study the approach to obtaining least squares solutions to systems of linear algebraic equations over networks by using distributed algorithms. Each node has access to one of the linear equations and holds a dynamic state. The aim for the node states is to reach a consensus as a least squares solution of the linear equations by exchanging their states with neighbors over an underlying intera...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

least squares solutions of inconsistent fuzzy linear matrix equations

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Least-squares collocation for linear higher-index differential-algebraic equations

Differential-algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differential-algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discreti...

Linear least squares localization in sensor networks

Localization in sensor networks is critical for search and rescue. Linear least squares (LLS) estimation is a sub-optimum but low-complexity localization algorithm based on measurements of location-related parameters. Commonly, there are two types of LLS localization algorithms using range measurements; one is based on introducing a dummy variable (called LLS-I), and the other is based on the s...