On the growth factor in Gaussian elimination for matrices with sharp angular field of values

Recently, the authors have shown that Gaussian elimination is stable for complex matrices A=B+iC where both B and C are Hermitian definite matrices. Moreover, the growth factor is less than [epsilon times the square root of 2] under any diagonal pivoting order. Assume now that B and C, in addition to being (positive) definite, satisfy the inequality C < or = [alpha]B, [alpha] > or = 0 i.e., [formula omitted]. If = 0, then A = B is a Hermitian positive definite matrix. It is well-known that, in this case, the growth factor is equal to 1. For [alpha] > 0, we establish a bound for the growth factor that has the limit 1 as [alpha maps into] 0. [PUBLICATION ABSTRACT]