Structural dependence in the incidence matrix associated with a system of equations may be used to detect misspecification of the underlying system. The incidence matrix can be represented as a bipartite graph G=(X,Y,E), with the node sets partitioned into the sets X1, X2, Y1 en Y2, such that (a) there are no edges between X1 en Y2, and (b) the cardinality of X1+Y2 is maximum. Such a partition corresponds with the detection of complete and maximal complementary subsets of structually dependent rows and columns. This problem is equivalent to finding a maximum independent vertex set or a minimum edge cover in thebipartite graph under the assumption of no isolated vertices. The problem of finding minimal and complete subsets of structurally dependent rows or columns is shown to be NP-complete. A heuristic approach for the detection of these minimal subsets based on Hall's transversal algorithm has worked satisfactorily in practice.

Structural dependence and systems of equations

The methodology of designing of analog circuits, being based on applications of control theory is basis for constructing of optimum or quasi optimal algorithm of designing. By a major criterion here, allowing to exposing the necessary structure of algorithm, there is a behavior of function of Lyapunov, which was defining for the process of optimization of circuit. Characteristics of function of Lyapunov and its derivative are basis for the search of optimum structure of control vector determining the structure of algorithm. The flow diagram of quasi optimal algorithm, realizing the basic ideas of the methodology is built, and basic characteristics of this algorithm are presented by comparison to traditional approach.

/pdf/preliminary-structure-of-quasi-optimal-algorithm-for-1r9dcek0ma.pdf

Preliminary structure of quasi optimal algorithm for optimization of analog circuits

Co-energy methods for elliptic flow and related problems

/pdf/network-partitioning-techniques-based-on-network-natural-d2rksxa4p8.pdf

Network partitioning techniques based on network natural properties for power system application

The structured decompositions for solving sparse nonlinear systems of equations are to transform the sparse systems into some special structures so that the computations can be decomposed efficiently for parallel processing. A group of structured nonlinear systems by decoinpositions and their parallel methods for solutions are overviewed.

Structured Decompositions for Solving Sparse Nonlinear Systems of Equations on Parallel Computers

Sparse Matrix Computations

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Sparse Matrix Computations

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Structural dependence and systems of equations

Preliminary structure of quasi optimal algorithm for optimization of analog circuits

Co-energy methods for elliptic flow and related problems

Network partitioning techniques based on network natural properties for power system application

Structured Decompositions for Solving Sparse Nonlinear Systems of Equations on Parallel Computers

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