| Operation | Calculation | Number of operations | Required storage |
| $m = m_{\mathrm{K}} = m_{\mathrm{M}}$ | $m = m_{\mathrm{K}}, m_{\mathrm{M}} = 0$ |
| Factorization of K | $\mathbf{K} = \mathbf{LDL}^{T}$ | $\frac{1}{2}nm^{2} + \frac{3}{2}nm$ | $\frac{1}{2}nm^{2} + \frac{3}{2}nm$ | |
| Subspace iteration | $\mathbf{K} \overline{\mathbf{X}}_{k+1} = \mathbf{Y}_{k}$ | $nq(2m + 1)$ | $nq(2m + 1)$ | |
| $\mathbf{K}_{k+1} = \overline{\mathbf{X}}_{l+1}^{T} \mathbf{Y}_{k}$ | $\frac{1}{2}nq(q + 1)$ | $\frac{1}{2}nq(q + 1)$ | |
| $\overline{\mathbf{Y}}_{k+1} = \mathbf{M} \overline{\mathbf{X}}_{k+1}$ | $nq(2m + 1)$ | $nq$ | |
| $\mathbf{M}_{k+1} = \overline{\mathbf{X}}_{l+1}^{T} \overline{\mathbf{Y}}_{k+1}$ | $\frac{1}{2}nq(q + 1)$ | $\frac{1}{2}nq(q + 1)$ | Algorithm is effectively implemented as out-of-core solver |
| $\mathbf{K}_{k+1} \mathbf{Q}_{k+1} = \mathbf{M}_{k+1} \mathbf{Q}_{k+1} \mathbf{A}_{k+1}$ | | $o(q^{3})$ neglected |
| $\mathbf{Y}_{k+1} = \overline{\mathbf{Y}}_{k+1} \mathbf{Q}_{k+1}$ | $nq^{2}$ | $nq^{2}$ |
| Sturm sequence check | $\overline{\mathbf{K}} = \mathbf{K} - \mu \mathbf{M}$ | $n(m + 1)$ | $n$ | |
| $\overline{\mathbf{K}} = \mathbf{LDL}^{T}$ | $\frac{1}{2}nm^{2} + \frac{3}{2}nm$ | $\frac{1}{2}nm^{2} + \frac{3}{2}nm$ | |
| Error* measures | $\frac{\|\mathbf{K}\phi_{i}^{(l+1)} - \lambda_{i}^{(l+1)} \mathbf{M}\phi_{i}^{(l+1)}\|_{2}}{\|\mathbf{K}\phi_{i}^{(l+1)}\|_{2}}$ | $4nm + 5n$ | $2nm + 5n$ | |
| Total for solution of $p$ lowest eigenvalues and associated eigenvectors, assuming that ten iterations are required and $q = \min \{2p, p + 8\}$ | $nm^{2} + nm(4 + 4p) + 5np + 20nq(2m + q + \frac{3}{2})$ | $nm^{2} + nm(3 + 2p) + 5np + 20nq(m + q + \frac{3}{2})$ | |
\*The error measures are not needed but may be of interest.
SUBROUTINE SSPACE (A, B, MAXA, R, EIGV, TT, W, AR, BR, VEC, D, RTOLV, BUP, BLO, SSP000011 BUPC, NN, NNM, NWK, NWM, NROOT, RTOL, NC, NNC, NITEM, IFSS, IFPR, NSTIF, IOUT) SSP00002
# PROGRAM
TO SOLVE FOR THE SMALLEST EIGENVALUES-- ASSUMED .GT. 0 -- AND CORRESPONDING EIGENVECTORS IN THE GENERALIZED EIGENPROBLEM USING THE SUBSPACE ITERATION METHOD
# -- INPUT VARIABLES --
| A(NWK) | = STIFFNESS MATRIX IN COMPACTED FORM (ASSUMED POSITIVE DEFINITE) |
| B(NWM) | = MASS MATRIX IN COMPACTED FORM |
| MAXA(NNM) | = VECTOR CONTAINING ADDRESSES OF DIAGONAL ELEMENTS OF STIFFNESS MATRIX A |
| R(NN,NC) | = STORAGE FOR EIGENVECTORS |
| EIGV(NC) | = STORAGE FOR EIGENVALUES |
| TT(NN) | = WORKING VECTOR |
| W(NN) | = WORKING VECTOR |
| AR(NNC) | = WORKING MATRIX STORING PROJECTION OF K |
| BR(NNC) | = WORKING MATRIX STORING PROJECTION OF M |
| VEC(NC,NC) | = WORKING MATRIX |
| D(NC) | = WORKING VECTOR |
| RTOLV(NC) | = WORKING VECTOR |
| BUP(NC) | = WORKING VECTOR |
| BLO(NC) | = WORKING VECTOR |
| BUPC(NC) | = WORKING VECTOR |
| NN | = ORDER OF STIFFNESS AND MASS MATRICES |
| NNM | = NN + 1 |
| NWK | = NUMBER OF ELEMENTS BELOW SKYLINE OF STIFFNESS MATRIX |
| NWM | = NUMBER OF ELEMENTS BELOW SKYLINE OF MASS MATRIX |
I. E. NWM=NWK FOR CONSISTENT MASS MATRIX
NWM=NN FOR LUMPED MASS MATRIX