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Complete pivoting growth of butterfly matrices and butterfly Hadamard matrices
John Peca-Medlin
The growth problem in Gaussian elimination (GE) remains a foundational question in numerical analysis and numerical linear algebra. Wilkinson resolved the growth problem in GE with…
Growth factors of orthogonal matrices and local behavior of Gaussian elimination with partial and complete pivoting
John Peca-Medlin
Gaussian elimination (GE) is the most used dense linear solver. Error analysis of GE with selected pivoting strategies on well-conditioned systems can focus on studying the behavio…
Distribution of the number of pivots needed using Gaussian elimination with partial pivoting on random matrices
John Peca-Medlin
Gaussian elimination with partial pivoting (GEPP) is a widely used method to solve dense linear systems. Each GEPP step uses a row transposition pivot movement if needed to ensure…
Growth factors of random butterfly matrices and the stability of avoiding pivoting
John Peca-Medlin, Thomas Trogdon
Random butterfly matrices were introduced by Parker in 1995 to remove the need for pivoting when using Gaussian elimination. The growing applications of butterfly matrices have oft…