Shinya Miyajima

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In this presentation, we are concerned with the accuracy of numerical solutions in the linear least squares problems min x∈R n b − Ax2, b ∈ R m , A ∈ R m×n (1) where m ≥ n or m < n. We assume that rank(A) = min(m, n). The problems (1) arises in many applications of scientific computations, e.g. linear and nonlinear programming [3], statistical analysis [2],(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)
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)