A New Proof 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.

• Qian-Ping Guo
• Hou-Biao Li

• CSPD matrix
• positive definite
• Schur complement
• Higham matrix
• Gaussian elimination
• Growth factor.

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