Bug: GMRES uses inconsistent convergence criteria in the outer and inner loops

[kakeueda]

Description how to reproduce the bug

The current GMRES implementation uses inconsistent convergence criteria in the outer and inner loops. The outer loop uses the criterion conv_cond while the inner loop always uses tol * ||r_0||.

Run a simple test using LinSolverIterativeFGMRES on the CPU with an identity right preconditioner and the following parameters:

• conv_cond = 0
• tol = 0.9
• restart = 2
• maxit = 10
• non-flexible GMRES

With conv_cond = 0 convergence should require the residual norm to be no greater than machine epsilon but the inner loop uses

tol_rel = tol * ||r_0|| ≈ 1.27279.

The inner loop terminates after one iteration because the estimated residual (~0.44721) is less than tol_rel.

$ ./gmres_convergence_test

=== inner criterion terminates conv_cond=0 ===
conv_cond=0 tol=0.9 restart=2 ||b||=1.41421
[MESSAGE] it 0: norm of residual 1.4142135623730951e+00 Norm of rhs: 1.4142135623730951e+00
[MESSAGE] it: 1 --> norm of the residual 4.4721359549995804e-01
[MESSAGE] End of cycle, ESTIMATED norm of residual 4.4721359549995804e-01
[MESSAGE] End of cycle, COMPUTED norm of residual 4.4721359549995793e-01

Re::Solve version

develop: 6038206

System and environment details

• Operating system: Ubuntu 24.04.4
• Compiler: GCC 13.3.0
• Backend: CPU
• Build configuration:
  • CUDA: enabled (CUDA 12.9), not used for this
  • KLU: enabled

Additional information

No response