Convergence of a Krylov solver

A quick demonstration that executable code works on this site. The residual of a Krylov method typically falls geometrically until it stagnates.

import matplotlib.pyplot as plt
import numpy as np

iterations = np.arange(0, 60)
residual = np.exp(-0.12 * iterations) + 1e-9

fig, ax = plt.subplots(figsize=(5.5, 3.4))
# "#750014" duplicates the $accent colour defined in theme.scss — matplotlib
# can't read SCSS variables, so if the site accent colour ever changes,
# update this literal to match.
ax.semilogy(iterations, residual, color="#750014", linewidth=1.6)
ax.set_xlabel("iteration")
ax.set_ylabel(r"$\|r_k\| / \|r_0\|$")
ax.grid(True, which="both", alpha=0.25)
fig.tight_layout()
plt.show()

Figure 1: Residual norm against iteration count.

The figure above was generated when this page was rendered, not pasted in.