An attainable upper matrix bound is derived for Σmk=1 (C + U1 + ... +Uk)-1Uk(C + U1 + ... + Uk)-1, improving upon earlier bounds by Anderson and Taylor [Linear Algebra Appl. 30:93-99 (1980)] and Olkin [Linear Algebra Appl. 52/53:529-532 (1983)]. Inequalities for the sum of harmonic means or parallel sums are derived as special cases. The more general problem of obtaining an upper bound for Σmk=1 (C + U1 + ... + Uk)-pUk(C + U1 + ... + Uk)-p is also considered.
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics