Heath, M. T.; Plemmons, R. J.; Ward, R. C. Sparse orthogonal schemes for structural optimization using the force method. (English) Zbl 0575.65031 SIAM J. Sci. Stat. Comput. 5, 514-532 (1984). The principle of the force (or flexibility) method which is used in matrix structural analysis and which is supposed to be carried out in two phases is given. A survey of basic methods to solve each of the two phases is given. An implementation of the method is proposed when turnback-QR procedure is used for phase 1 and Paige’s linearly constrained sum-of-squares procedure for phase 2. Such usage of orthogonal factorization techniques preserves sparsity for large-scale problems and maintains numerical stability. Reviewer: L.Bakule Cited in 23 Documents MSC: 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65K05 Numerical mathematical programming methods 74S30 Other numerical methods in solid mechanics (MSC2010) Keywords:structural optimization; force method; orthogonal factorization; Givens rotations; turnback-QR method; sparse least squares; constrained sum-of- squares method Software:Y12M PDFBibTeX XMLCite \textit{M. T. Heath} et al., SIAM J. Sci. Stat. Comput. 5, 514--532 (1984; Zbl 0575.65031) Full Text: DOI