Group Inverses of M-Matrices and Their Applications

ISBN: 9781439888582 出版年：2012 页码：330 Kirkland, Stephen J Neumann, Michael CRC Press

Motivation and Examples An example from population modelling An example from Markov chains The Group Inverse Definition and general properties of the group inverse Spectral properties of the group inverse Expressions for the group inverse Group inverse versus Moore-Penrose inverse The group inverse associated with an M-matrix Group Inverses and Derivatives of Matrix Functions Eigenvalues as functions First and second derivatives of the Perron value Concavity and convexity of the Perron value First and second derivatives of the Perron vector Perron Eigenpair in Demographic Applications Introduction to the size-classified population model First derivatives for the stage-classified model Second derivatives of the Perron value in the age-classified model Elasticity and its derivatives for the Perron value The Group Inverse in Markov Chains Introduction to Markov chains Group inverse in the periodic case Perturbation and conditioning of the stationary distribution vector Bounds on the subdominant eigenvalue Examples Mean First Passage Times for Markov Chains Mean first passage matrix via the group inverse A proximity inequality for the group inverse The inverse mean first passage matrix problem A partitioned approach to the mean first passage matrix The Kemeny constant Applications of the Group Inverse to Laplacian Matrices Introduction to the Laplacian matrix Distances in weighted trees Bounds on algebraic connectivity via the group inverse Resistance distance, the Weiner index and the Kirchhoff index Interpretations for electrical networks Computing the Group Inverse Introduction The shuffle and Hartwig algorithms A divide and conquer method Stability issues for the group inverse Bibliography