On the growth factor in Gaussian elimination for generalized Higham matrices

Abstract

AbstractA Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite. We prove that, for such A, the growth factor in Gaussian elimination is less than 3. Moreover, a slightly larger bound $${3\sqrt{2}}$$ holds true for a broader class of complex matrices A=B+iC, where B and C are Hermitian and positive definite. Copyright © 2002 John Wiley & Sons, Ltd.