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Full-Text Articles in Physical Sciences and Mathematics
Computational Algebra Applications In Reliability, G Hartless, Lawrence Leemis
Computational Algebra Applications In Reliability, G Hartless, Lawrence Leemis
Arts & Sciences Articles
Reliability analysts are typically forced to choose between using an 'algorithmic programming language' or a 'reliability package' for analyzing their models and lifetime data. This paper shows that computational languages can be used to bridge the gap to combine the flexibility of a programming language with the ease of use of a package. Computational languages facilitate the development of new statistical techniques and are excellent teaching tools. This paper considers three diverse reliability problems that are handled easily with a computational algebra language: system reliability bounds; lifetime data analysis; and model selection.
Structured Eigenvectors, Interlacing, And Matrix Completions, Brenda K. Kroschel
Structured Eigenvectors, Interlacing, And Matrix Completions, Brenda K. Kroschel
Dissertations, Theses, and Masters Projects
This dissertation presents results from three areas of applicable matrix analysis: structured eigenvectors, interlacing, and matrix completion problems. Although these are distinct topics, the structured eigenvector results provide connections.;It is a straightforward matrix calculation that if {dollar}\lambda{dollar} is an eigenvalue of A, x an associated structured eigenvector and {dollar}\alpha{dollar} the set of positions in which x has nonzero entries, then {dollar}\lambda{dollar} is also an eigenvalue of the submatrix of A that lies in the rows and columns indexed by {dollar}\alpha{dollar}. We present a converse to this statement and apply the results to interlacing and to matrix completion problems. Several corollaries …