Sensitivities of multiple singular values for optimal geometries of precision structures (Q1302184)

The authors compute the sensitivities of a repeated singular value of a matrix with respect to parameters affecting the matrix. The technique is an outgrowth of a similar approach for computing the sensitivities of an eigenvalue of square matrix. It is shown that the derivatives can be obtained under the condition that the parameters change is in a direction which maintains the order of multiplicity of the singular value. The method is tested on the design of geometry of a precision truss subjected to a family of disturbances. Two examples are presented: a case with a single singular value, and a case where the first singular value merges with the initially distinct climbing second singular value.