24-311: Numerical Methods
Recitation 6: Exam 1 review
Numerical methods so far...
Taylor series
f(x_0 + x) = f(x_0)\\
\hspace{10em}+ \frac{(x-x_0)^1}{1!} f'(x_0)\\
\hspace{10em}+ \frac{(x-x_0)^2}{2!} f''(x_0)\\
\hspace{10em}+ \frac{(x-x_0)^3}{3!} f'''(x_0)\\
\hspace{10em}+ \cdots\\
\hspace{10em}+ \frac{(x-x_0)^n}{n!} f^{(n)}(x_0)\\
Root finding: bisection method
Given \(f(x)\), find \(x\) such that \(f(x) = 0\)
1 new function evaluation at every incremental step
Root finding: false position method
Given \(f(x)\), find \(x\) such that \(f(x) = 0\)
1 new function evaluation at every incremental step
Optimization: gradient descent
Given \(f(x)\), find its minima
Optimization: gradient descent
Given \(f(x)\), find its minima
Download this file!