Convergence of The Barzilai-Borwein Method for Solving Slightly Unsymmetric Linear Systems

Abstract

Due to its simplicity and numerical efficiency, the Barzilai and Borwein (BB) gradient method has received numerous attentions in different scientific fields. In this paper, the sufficient condition for convergence of the BB method when the coefficient matrix of linear algebraic equations is slightly unsymmetric with positive definite symmetric part is presented

Keywords

• Unsymmetric linear algebraic equations
• Barzilai and Borwein gradient method
• symmetric and skew-symmetric matrices
• eigenvalues
• condition number