On the growth factor in Gaussian elimination for generalized Higham matrices

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3 √ 2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some new findings. Keywords—CSPD matrix, positive definite, Schur complement, Higham matrix, Gaussian elimination, Growth factor.