Compact form of the pseudo-inverse matrix in the approximation of a star graph using the conductance electrical model (CEM)
Document typeConference report
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The Conductance Electrical Model (CEM) translate a graph into a circuit. After applying the model, in many cases, it is necessary to approximate the circuit obtained by a star circuit and this requires the calculation of the Moore–Penrose pseudoinverse of a matrix for which there is a general formula that requires transpose, multiply and invert matrices. But in this particular case, the matrix has a peculiar struc- ture, exploited this peculiar structure in this paper show that the pseu- doinverse can be obtained without recourse to the general formula. We demonstrate a closed formula that gives the values of the elements of the pseudoinverse directly without iteration, no longer necessary to multiply or inverter matrices. This improved method eliminates the problems due to computer rounding and due to bad-conditioned problems in mathe- matical terms.
CitationIgelmo, M.; Sanfeliu, A. Compact form of the pseudo-inverse matrix in the approximation of a star graph using the conductance electrical model (CEM). A: IAPR International Workshop on Syntactic and Strutural Pattern Recognition. "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)". 2012, p. 539-547.
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