From cdf6be9e545f097c0ecd46cd2be716c84f729a0b Mon Sep 17 00:00:00 2001 From: Christian Kolset Date: Tue, 9 Sep 2025 15:26:03 -0600 Subject: Added image --- tutorials/module_3/2_roots_optimization.md | 4 ++-- tutorials/module_3/bisection.png | Bin 0 -> 145156 bytes 2 files changed, 2 insertions(+), 2 deletions(-) create mode 100644 tutorials/module_3/bisection.png (limited to 'tutorials') diff --git a/tutorials/module_3/2_roots_optimization.md b/tutorials/module_3/2_roots_optimization.md index 83684d5..cc9dbb5 100644 --- a/tutorials/module_3/2_roots_optimization.md +++ b/tutorials/module_3/2_roots_optimization.md @@ -59,8 +59,8 @@ Let's consider a continuous function $f(x)$ with an unknown root $x_r$ . Using t Once we bisect the interval and found we set the new predicted root to be in the middle. We can then compare the two sections and see if there is a sign change between the bounds. Once the section with the sign change has been identified, we can repeat this process until we near the root. -![[Pasted image 20250905120647.png|500]] -As you the figure shows, the predicted root $x_r$ get's closer to the actual root each iteration. In theory this is an infinite process that can keep on going. In practice, computer precision may cause error in the result. A work-around to these problems is setting a tolerance for the accuracy. As engineers it is our duty to determine what the allowable deviation is. +![[bisection.png|500]] +As you the figure shows, the predicted root $x_r$ get's closer to the actual root each iteration. In theory this is an infinite process that ca3n keep on going. In practice, computer precision may cause error in the result. A work-around to these problems is setting a tolerance for the accuracy. As engineers it is our duty to determine what the allowable deviation is. So let's take a look at how we can write this in python. ```python diff --git a/tutorials/module_3/bisection.png b/tutorials/module_3/bisection.png new file mode 100644 index 0000000..e561962 Binary files /dev/null and b/tutorials/module_3/bisection.png differ -- cgit v1.2.3