Abstract
Some of the completion problems considered so far referred to matrices with specified entries lying about the main diagonal. It turns out that the tentative to approach similar problems for matrices with sparse specified entries leads to connections with certain classes of graphs. In this chapter we show some of these connections, especially emphasizing the role played by the chordal graphs in the extension of some of the results concerning the band matrices. Partial matrices which admit positive or contractive completions are studied in more details. Besides, it is pointed out that the Schur parameters still play a certain role in this direction.
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© 1996 Birkhäuser Verlag
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Constantinescu, T. (1996). Graphs and Completion Problems. In: Schur Parameters, Factorization and Dilation Problems. Operator Theory Advances and Applications, vol 82. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9108-0_7
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DOI: https://doi.org/10.1007/978-3-0348-9108-0_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9910-9
Online ISBN: 978-3-0348-9108-0
eBook Packages: Springer Book Archive