Abstract : This report summarizes the activities at Boeing Computer Service Company from April 15, 1985 until August 15, 1986. Five tasks are defined in our analysis of quotient tree algorithms and frontal methods: analysis of multifrontal methods, creation of symmetric indefinite out - of-core minimal storage elimination schemes, analyses of quotient tree orderings, and completion of the Boeing-Harwell sparse matrix collection. (Keywords: linear equations; reordering algorithms; Choleski factorization; vector computers; parallel computers.