Sentence:  Suppose that there were no <WSD>fill-ins</WSD> added in the course of factorization. (This is unrealistic, but we have developed techniques to minimize the number of <WSD>fill-ins</WSD> and in practice the number of <WSD>fill-ins</WSD> may be relatively small.) 
Meaning of the word marked with <WSD> tags:  An intermediate result that must be stored temporarily during the course of a sparse matrix computation.