Let A be an nxn real symmetric diagonal dominant matrix with positive diagonal part D, let S^2=D-1 and H=SAS. The following relation between the condition number k(H)=||H-1|| ||H|| and the spectral radius r of the Jacobi matrix associated to A is proved.
Relations between condition numbers and the convergence of the Jacobi method for real positive definite matrices
1982
Abstract
Let A be an nxn real symmetric diagonal dominant matrix with positive diagonal part D, let S^2=D-1 and H=SAS. The following relation between the condition number k(H)=||H-1|| ||H|| and the spectral radius r of the Jacobi matrix associated to A is proved.File in questo prodotto:
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Descrizione: Relations between condition numbers and the convergence of the Jacobi method for real positive definite matrices
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