Actuator Placement Optimization by Genetic and Improved Simulated Annealing Algorithms

Concluding Remarks The following have been mathematically proven and shown by a numerical example: 1) SVD, as is well known, is a very strong numerical analysis tool for solving ill-conditioned linear equations, but it can be computationally costly when there is only small rank deficiency. 2) As was shown here, ED is a first-order approximation of SVD, and as was shown in Ref. 2, ED is computationally very efficient for large matrices with small rank deficiency, because only the first nonzero and all zero eigenvalues and eigenvectors are required. 3) As has been shown in this Note, SED is a second-order approximation of SVD and only requires the solution of two sets of linear equations. However, unless one obtains the first nonzero eigenvalue, the errors involved will be difficult to bound accurately.