Error Bound of the Multilevel Adaptive Cross Approximation (MLACA).

An error bound of the multilevel adaptive cross approximation (MLACA), which is a multilevel version of the adaptive cross approximation-singular value decomposition (ACA-SVD), is rigorously derived. For compressing an off-diagonal submatrix of the method of moments (MoM) impedance matrix with a binary tree, the $L$-level MLACA includes L+1$ steps, and each step includes 2^L$ ACA-SVD decompositions. If the relative Frobenius norm error of the ACA-SVD used in the MLACA is smaller than \varepsilon $, the rigorous proof in this communication shows that the relative Frobenius norm error of the L. In practical applications, the error bound of the MLACA can be approximated as \varepsilon (L + 1)$, because \varepsilon $ is always \ll 1$. The error upper bound can be used to control the accuracy of the MLACA. To ensure an error of the L$-level MLACA smaller than \varepsilon , which approximately equals {\varepsilon/{(L + 1)}} for practical applications. [ABSTRACT FROM AUTHOR]