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Table 3 Optimal parameter \(\nu _{\eta }\) of Theorem 1, with \(\eta =1\) and condition numbers of matrices for the cylinder problems

From: Application of an iterative Golub-Kahan algorithm to structural mechanics problems with multi-point constraints

 

\(\varvec{\lambda _1} \)

\(\varvec{\lambda _n} \)

\(\varvec{\nu _{\eta }}\)

\(\varvec{\kappa \, ({\tilde{\mathbf{A }}})^{2}}\)

iter

\(\varvec{\kappa }\) (M)

Prob. 1

0.06

114.4

16.7

2.00

11

\(3.9.10^5\)

Prob. 2

\(7.6.10^{-3}\)

450.2

132.4

1.99

9

\(2.8.10^7\)

Prob. 3

\(2.8.10^{-3}\)

\(1.0.10^3\)

356.2

1.99

8

\(3.1.10^8\)