Saddle point problems, Bott-Duffin inverses, abstract splines and oblique projections

In this note, we present links between several different areas in numerical analysis and operator theory. More precisely, we show that several saddle point problems are solvable in the presence of a property (called compatibility) between a positive operator and a closed subspace of a Hilbert space, and the same happens with certain abstract spline problems. These notions are related to the generalized Bott?Duffin inverse.Fil: Arias, Maria Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; ArgentinaFil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Matematicas; ArgentinaFil: Gonzalez, Maria Celeste. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina. Universidad Nacional de General Sarmiento; Argentin

A Note on Computing the Generalized Inverse A^(2)_{T,S} of a Matrix A

The generalized inverse A T,S (2) of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A T,S (2) has been recently developed with the condition σ (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose inverse A M,N † and the Drazin inverse AD. Numerical examples are given to illustrate our results

Generalized inverse of a matrix and its applications

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