Graphs and Completion Problems
T. Constantinescu · Birkhäuser Basel eBooks · 1996
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. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.