week 9: root finders

_announcements/week-9.md

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+---
+title: Week 9 Announcement
+week: 9
+date: 2024-03-18
+---
+
+A common problem is to find the roots of an equation. We will develop
+two algorithms to find roots numerically. The *bisection* algorithm is
+a simple and robust approach that exemplifies how to go from imagining
+a solution ("how would I solve this problem?") to an actual
+implementation. We then will develop a much faster but less robust
+algorithm known as *Newton-Raphson*. In both cases we will initially
+restrict ourselves to 1D problems but we will later extend
+Newton-Raphson to arbitrary dimensions (once we learned how to solve
+matrix problems).