Abstract
Expressions which include the Moore-Penrose (MP) inverse with various generalized inverses have been popular topic in numerical linear algebra. The most general case was the combination of the MP inverse with outer inverses AR(B),N(C)(2), known as the composite outer inverses. Starting from well-known and useful Urquhart representation of generalized inverses, in this research we consider Φ1-composite outer inverses which are based on the replacements of AR(B),N(C)(2) by the more general expressions Φ1:=B(CAB)(1)C. Algorithms for symbolic and numeric computation of Φ1-composite outer inverses are proposed and corresponding examples are developed. In addition, Φ2-composite outer inverses arising from the replacements of the term AR(B),N(C)(2) in composite outer inverses by the expressions Φ2:=B(CAB)(2)C∈A{2}, are investigated.
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