1
vote
1answer
24 views

division by sum of exponentials of large negative numbers

I need to evaluate the following numerically: $$ f = \frac{\exp(a)}{\exp(a)+\exp(b)+\exp(c) + \exp(d)} $$ $a,b,c$ and $d$ are large negative numbers, they are smaller than -1000. Numerically ...
3
votes
4answers
117 views

Computing a large exp(x) in a numerically robust way.

I'm trying to compute $\lfloor e^x \rfloor$, where x is a 64-bit integer. The problem is that the result of the computation may be close to 2^64. In this range, 64-bit floating point numbers will be ...
1
vote
1answer
114 views

Error analysis of exponential function

By definition: $$ e^x = \lim_{n \rightarrow \infty} ( 1 + \frac{x}{n} ) ^ n$$ I am interesting in calculating the error $$\left | e^x - \left( 1 + \frac{x}{n} \right) ^ n \right|$$ for some fixed $n ...
1
vote
0answers
126 views

Stable solution of nonlinear equation

I'm trying to numerically solve equation for $t\in \mathbb{R}$ $$ n \cdot e^{At}x_0= c $$ $A \in \mathbb{R^{3\times 3}},n,x_0 \in \mathbb{R^3}, c \in \mathbb{R}$. I'm looking for smallest positive ...
0
votes
1answer
556 views

Problem to find the intersection of a exponential and linear function

I have the problem to find the intersection of a exponential and linear function. My math teacher can't help me, but I'm interested how I can solve this. I tried to use the equating method, but it ...
0
votes
0answers
91 views

How to solve $a(\exp(b/x)-1)=c(\exp(b/(x-d))-1)$ for $x$?

How to solve $a(\exp\left(\frac{b}{x}\right)-1)=c(\exp\left(\frac{b}{x-d}\right)-1)$ for $x$? where $a,b,c,d$ can be treated as constants. This problem is a simplified version of dividing the ...
1
vote
1answer
296 views

Identifying when exponential function argument has doubled or tripled

Suppose that I have a function $f(k) = U\exp(k)$. Suppose also that I know $f(k)$, but not $k$ or $U$. I modify this function as shown below, and take $k= k_0$ and $U$ as fixed constants: ...
0
votes
1answer
46 views

Determining presence or absence of function in expression

Suppose that I am given ${\tilde U_1,\ldots,\tilde U_N}$ as a sequence of numbers, and in addition, $U_1,\ldots,U_N$ is unknown, and $q$ is unknown and constant for all ${\tilde U_1,\ldots,\tilde ...