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Least Squares Approximate and Least Norm Solutions of Paired Singular Equations
Author(s) -
Speck FrankOlme
Publication year - 1987
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19871300104
Subject(s) - mathematics , invertible matrix , moore–penrose pseudoinverse , factorization , singular integral , hilbert space , projector , norm (philosophy) , mathematical analysis , pure mathematics , singular value , inverse , integral equation , eigenvalues and eigenvectors , physics , geometry , algorithm , quantum mechanics , computer science , political science , law , computer vision
Paired operators T = A 1 P + A 2 Q on a H ILBERT space are studied where P is a projector, P + Q = I , and the coefficients are linear invertible operators. The M OORE ‐P ENROSE inverse of T can be obtained explicitly from a factorization of the coefficients, which is equivalent to the normal solvability of T and occurs in numerous applications. As an example, systems of singular integral equations of C AUCHY type are analysized in detail.