Rump, Siegfried M.Siegfried M.RumpOishi, Shin’ichiShin’ichiOishi2024-10-072024-10-072024-02-09Japan Journal of Industrial and Applied Mathematics 41 (2): 1097-1104 (2024)https://hdl.handle.net/11420/49388Recently Oishi published a paper allowing lower bounds for the minimum singular value of coefficient matrices of linearized Galerkin equations, which in turn arise in the computation of periodic solutions of nonlinear delay differential equations with some smooth nonlinearity. The coefficient matrix of linearized Galerkin equations may be large, so the computation of a valid lower bound of the smallest singular value may be costly. Oishi’s method is based on the inverse of a small upper left principal submatrix, and subsequent computations use a Schur complement with small computational cost. In this note some assumptions are removed and the bounds improved. Furthermore a technique is derived to reduce the total computationally cost significantly allowing to treat infinite dimensional matrices.en0916-70052024210971104Springerhttps://creativecommons.org/licenses/by/4.0/65F45Bound for the norm of the inverse of a matrixGalerkin’s equationMinimum singular valueNonlinear delay differential equationSchur complementNatural Sciences and Mathematics::510: MathematicsJournal Article10.15480/882.1337310.1007/s13160-024-00645-710.15480/882.13373Journal Article