Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems

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 proposed method. As an application of the proposed method, an efficient method of enclosing all eigenpairs in the quadraticeigenvalue problem is also sketched.

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