Takeshi Terao

activity

20242026

collaborators

5 papers

math.NA2026

Iterative Refinement for Diagonalizable Non-Hermitian Eigendecompositions

Takeshi Terao

This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distingui…

math.NA2026

Iterative Refinement for a Subset of Eigenvectors of Symmetric Matrices via Matrix Multiplications

Takeshi Terao, Katsuhisa Ozaki, Toshiyuki Imamura +1

We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ( $k ≪ n$ ) of an $n \times n$ real symmetric matrix. Using an orthog…

math.NA2026

Forward Error-Oriented Iterative Refinement for Eigenvectors of a Real Symmetric Matrix

Takeshi Terao, Katsuhisa Ozaki

In this paper, we discuss numerical methods for the eigenvalue decomposition of real symmetric matrices. While many existing methods can compute approximate eigenpairs with suffici…

math.NA2025

Verified error bounds for the singular values of structured matrices with applications to computer-assisted proofs for differential equations

Takeshi Terao, Yoshitaka Watanabe, Katsuhisa Ozaki

This paper introduces two methods for verifying the singular values of the structured matrix denoted by $R^{- H} A R^{- 1}$ , where $R$ is a nonsingular matrix and $A$ is a general nons…

math.NA2024

Method for Verifying Solutions of Sparse Linear Systems with General Coefficients

Takeshi Terao, Katsuhisa Ozaki

This paper proposes a verification method for sparse linear systems $A x = b$ with general and nonsingular coefficients. A verification method produces the error bound for a given app…