منابع مشابه
New results on the quasi-commuting inverses
A matrix has an ordinary inverse only if it is square, and even then only if it is nonsingular or, inother words, if its columns (or rows) are linearly independent. In recent years needs have been felt innumerous areas of applied mathematics for some kind of partial inverse of a matrix that is singularor even rectangular. In this paper, some results on the Quasi-commuting inverses, are given an...
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In this paper we derive a successive matrix squaring (SMS) algorithm to approximate an outer generalized inverse with prescribed range and null space of a given matrix A ∈ Cm×n r . We generalize the results from the papers [3], [16], [18], and obtain an algorithm for computing various classes of outer generalized inverses of A. Instead of particular matrices used in these articles, we use an ap...
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This paper deals with the algorithm for computing outer inverse with prescribed range and null space, based on the choice of an appropriate matrix G and Gauss–Jordan elimination of the augmented matrix [G | I]. The advantage of such algorithms is the fact that one can compute various generalized inverses using the same procedure, for different input matrices. In particular, we derive representa...
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We present a local convergence analysis of generalized Newton methods for singular smooth and nonsmooth operator equations using adaptive constructs of outer inverses. We prove that for a solution x of F(x) = 0, there exists a ball S = S(x ; r), r > 0 such that for any starting point x 0 2 S the method converges to a solution x 2 S of ?F (x) = 0, where ? is a bounded linear operator that depend...
متن کاملGroup Inverses and Drazin Inverses over Banach Algebras
For a matrix over a complex commutative unital Banach algebra, necessary and suucient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earl...
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ژورنال
عنوان ژورنال: Advances in Linear Algebra & Matrix Theory
سال: 2013
ISSN: 2165-333X,2165-3348
DOI: 10.4236/alamt.2013.34013