Distributed least squares solver for network linear equations

• In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We first propose a distributed least square solver over connected undirected interaction graphs and establish a necessary and sufficient on the step-size under which the algorithm exponentially converges to the least square solution. Next, we develop a distributed least square solver over strongly connected directed graphs and show that the proposed algorithm exponentially converges to the least square solution provided the step-size is sufficiently small. Moreover, we develop a finite-time least square solver by equipping the proposed algorithms with a finite-time decentralized computation mechanism. The theoretical findings are validated and illustrated by numerical simulation examples.

Ämnesord

NATURVETENSKAP  -- Kemi -- Polymerkemi (hsv//swe)

NATURAL SCIENCES  -- Chemical Sciences -- Polymer Chemistry (hsv//eng)

Nyckelord

Distributed algorithms

Dynamical systems

Finite-time computation

Least squares

Linear equations

Directed graphs

Linear algebra

Linear networks

Parallel algorithms

Finite time

Interaction graphs

Least Square

Least-square solution

Linear algebraic equation

Step size

Strongly connected

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