2 votes
Accepted

Exercise with a fixed point iteration

It is easy to prove from $f(x)$ being positive but strictly decreasing over all $\mathbb R$ that any negative number maps to a positive number in one iteration any nonnegative number maps to a number ...
  • 92.2k
2 votes

Stiff system of ODEs with known exact solutions

Using the wonderful notes "STUDENT VERSION, Stiff Differential Equations" by Kurt Bryan Example 1 As you noted, the simplest example is to just create a diagonal system $$y_1(t) = \lambda_1 ...
  • 9,850
2 votes
Accepted

Number of iterations with a fixed point problem

Hint For $k \ge 1$, you have using the Mean Value Theorem, and the fact that $z^* = f(z_*)$ $$\begin{aligned} \lVert z_{k+1} - z^* \rVert &= \lVert f(z_k) - f(z^*)\rVert\\ &\le M \lVert z_{k} ...
1 vote

Prerequisites for Computational Mathematics

Depends on what sort of field you want to learn about. I would recommend taking an intro to "Numerical Analysis" course, which usually just requires a basic proofs/calculus background. ...
  • 3,799
1 vote

Enumeration of floating point numbers

Taking $\beta = 10, t = 1, L=-1, U=1$, we have that \begin{align*} \mathbb{F} =& \{0.1\times 10^{-1}, 0.2 \times 10^{-1},\cdots, 0.9 \times 10^{-1}, \\ &0.1 \times 10^0, 0.2\times 10^0, \...
  • 16.6k

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