# Implicit standard Jacobi gives high relative accuracy

@article{Dopico2009ImplicitSJ,
title={Implicit standard Jacobi gives high relative accuracy},
author={F. Dopico and P. Koev and J. M. Molera},
journal={Numerische Mathematik},
year={2009},
volume={113},
pages={519-553}
}
• Published 2009
• Mathematics, Computer Science
• Numerische Mathematik
We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDXT of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. The relative error in every eigenvalue is bounded by $${O(\epsilon \kappa (X))}$$ , where $${\epsilon}$$ is the machine precision and $${\kappa(X)\equiv\|X\|_2\cdot\|X^{-1}\|_2}$$ is the spectral condition number of X. The eigenvectors are also computed accurately in the appropriate… Expand
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