American Jazz Institute

The exact maximum growth factor for complete pivoting on real 5 × 5 matrices

Abstract Let ρ₅ᴿ be the largest element growth possible in exact Gaussian elimination with complete pivoting on real 5 × 5 matrices, with every legal choice at a pivot tie allowed. We prove ρ₅ᴿ = α = 4.132517078632472854223346853277…, where α is the algebraic lower bound identifi...