4 papers
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 eigenvectors () of an real symmetric matrix. Using an orthog…
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…
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 , where is a nonsingular matrix and is a general nons…
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 with general and nonsingular coefficients. A verification method produces the error bound for a given app…