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Questions related to whether the sequence of iterates generated by an iterative method has one or more limit points, and if those limit points have the correct properties.

2 votes
2 answers
2k views

Implementing Gelfand’s formula for the spectral radius in Python - lack of convergence

For context: Gelfand's formula for the spectral radius is $\lim_{k\rightarrow \infty}|A^k|^{1/k}$ where $|\cdot|$ is any well-defined operator norm. I naively coded a function to calculate the $k$th …
Martin C.'s user avatar
  • 229
1 vote
Accepted

Implementing Gelfand’s formula for the spectral radius in Python - lack of convergence

8]]) for k in range(1, 100): term = kth_term(a, k) print("k={}: {}".format(k, term)) plt.plot(k, term, 'rx') plt.plot(k, term, 'rx', label="kth term") plt.title("Convergence
Martin C.'s user avatar
  • 229