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Two types of error bounds are considered for numerically enclosing all eigen-values of a matrix. A theorem is presented for clarifying the relation between these two error bounds under an assumption. We discuss the validity of this assumption, and report some numerical results illustrating the presented theorem and showing that this assumption is satisfied… (More)

In stationary iterative methods for solving linear systems Ax = b, the iteration x (k+1) = Hx (k) + c, where H and c are the iteration matrix derived from A and the vector derived from A and b, respectively, is executed for an initial vector x (0). We present a theorem which yields componentwise error estimates for x (k) , and clarify the relation between… (More)

A fast method for enclosing all eigenpairs in symmetric positive definite generalized eigenvalue problems is proposed. Firstly theorems on verifying all eigenvalues are presented. Next a theorem on verifying all eigenvectors is presented. The proposed method is developed based on these theorems. Numerical results are presented showing the efficiency of the… (More)