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Computational Aspects of the Greatest Lower Bound to the Reliability and Constrained Minimum Trace Factor Analysis
Jos M. F. ten Berge, Tom A. B. Snijders, Frits E. Zegers
Journal:

Psychometrika / Volume 46 / Issue 2 / June 1981

Published online by Cambridge University Press:

01 January 2025, pp. 201-213
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In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.

Inequalities on partial traces of positive semidefinite block matrices
Part of
- Basic linear algebra
- Special classes of linear operators
Xiaohui Fu, Pan-Shun Lau, Tin-Yau Tam
Journal:

Canadian Mathematical Bulletin / Volume 64 / Issue 4 / December 2021

Published online by Cambridge University Press:

18 December 2020, pp. 964-969

Print publication:

December 2021
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Inequalities on partial traces of positive semidefinite matrices are studied. Extensions of several existing inequalities on the determinant of partial traces are then obtained. Particularly, we improve a determinantal inequality given by Lin [Canad. Math. Bull. 59(2016)].

Chapter Eight - Wave-Energy Converter Arrays
Johannes Falnes, Adi Kurniawan
Book:

Ocean Waves and Oscillating Systems

Published online:

12 May 2020

Print publication:

28 May 2020, pp 262-292
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Summary

Chapter 8 concerns a group of WEC units that may be realised in a more distant future, namely groups or arrays of individual WEC units and two-dimensional WEC units, which needs to be rather big structures. Firstly, a group of WEC bodies is analysed. Next a group consisting of WEC bodies as well as OWCs is analysed. Then the previous real radiation resistance needs to be replaced by a complex radiation damping matrix which is complex, but Hermitian, which means that its eigenvalues are real.