Richard Rosen

Structural analysis by matrix decomposition

Abstract A physical interpretation is derived for the Choleski decomposition method as applied to structural analysis. Both the stiffness (displacement) and flexibility (force) methods of structural analysis are treated. The interpretation is shown to be valuable in providing physically meaningful upper and lower bounds on the elements of the decomposed diagonal matrix. These bounds are useful in error analysis of structural computations on a digital computer.

Error analysis in structural computations

Abstract The errors in structural computations are assessed and bounds are established on their magnitude. The matrix decomposition approach is shown to be most useful in error analysis. Both positive definite and positive semi-definite matrices are treated. The discrete finite-digit representation of numbers in a digital computer and the nature of digital computer calculations are considered in the development.