Using QR factorization and SVD to solve input estimation problems in structural dynamics

Input estimation problems in structural mechanics are in general ill-posed. Treatment of these problems requires that the problems are reformulated, usually by numerical regularization techniques. Several methods of solving input estimation problems, which take the form of structured block matrix problems, are studied in this paper. The investigated methods are based on forming the normal equations, QR factorization and singular value decomposition. A specific block QR factorization algorithm utilizing the structure of the associated upper block triangular Toeplitz matrix is also introduced. Moreover, a criterion for choosing the level of regularization based on the data used to construct L-curves is suggested. Numerical examples are given to illustrate various numerical aspects of the different methods and the performance of the advocated criterion.