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SYNC: update calvo_machine_learn.md from lecture-python-advanced.myst #13

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mmcky merged 2 commits into from
May 28, 2026
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SYNC: update calvo_machine_learn.md from lecture-python-advanced.myst #13

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SYNC: update calvo_machine_learn.md from lecture-python-advanced.myst
mmcky May 28, 2026
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Merge branch 'main' into sync-calvo-machine-learn-from-source
mmcky May 28, 2026
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16 changes: 3 additions & 13 deletions lectures/calvo_machine_learn.md
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Expand Up @@ -139,21 +139,11 @@ or

Because $\alpha > 0$, $0 < \frac{\alpha}{1+\alpha} < 1$.

```{prf:definition}
:label: square-summable

For scalar $b_t$, let $L^2$ be the space of sequences
$\{b_t\}_{t=0}^\infty$ that satisfy
We assume that the sequence $\vec \mu = \{\mu_t\}_{t=0}^\infty$ is bounded.

$$
\sum_{t=0}^\infty b_t^2 < +\infty
$$

We say that a sequence that belongs to $L^2$ is **square summable**.
```

When we assume that the sequence $\vec \mu = \{\mu_t\}_{t=0}^\infty$ is square summable and also require that the sequence $\vec \theta = \{\theta_t\}_{t=0}^\infty$ is square summable,
the linear difference equation {eq}`eq_grad_old2` can be solved forward to get:

Then the linear difference equation {eq}`eq_grad_old2` can be solved forward to get:

```{math}
:label: eq_grad_old3
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