article Open Access
A study of measuring the distance of a stable matrix to the unstable matrices
International Journal of Statistics and Applied Mathematics · 2018 · Vol. 3(2) · pp. 285–288
Abstract
This paper determine the 2-norm and frobenius norm distance form a given matrix A to the nearest matrix, we explain a bisection method due to Byers, with an Eigen value on the imaginary axis. If A has an Eigen value plane, then, this distance measures how “nearly unstable” A is. Each bisection step provides a rigorous upper bound or lower bound on the distance. Here, we use Bayer’s Bisection method to estimate the distance to the nearest matrix with an Eigen value on the unit circle.
Matrix Theory and AlgorithmsAdvanced Optimization Algorithms ResearchControl Systems and IdentificationMathematicsMatrix normUnit circleMatrix (chemical analysis)Complex planeUpper and lower boundsEigenvalues and eigenvectorsBisection methodDistance matrixBisection
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