1
vote
1answer
41 views

Constrained Newton-Raphson method

Peace be upon you, I want to solve a system of two equations in which the existence of $ln\left(\frac{\alpha}{\alpha+\beta}\right)$ function makes some limitations in iterations of the Newton-Raphson ...
1
vote
0answers
32 views

Approximations for finite n in limit-based definition of the exponential function

The exponential function can be defined via: $$ e^x = \lim_{n \rightarrow \infty} \left( 1 + \frac{x}{n} \right)^{n} = \lim_{n \rightarrow \infty} g(x; n) $$ In my problem, I actually have the right ...
2
votes
1answer
21 views

normal equations of $ y(t) = \gamma e^{\lambda t} $ for minimizing the error

Let $ y(t) = \gamma e^{\lambda t} $ and we have the points $(0,2)\ (1,0.7)\ (3, 0.3)$. The task is to get the parameter so that error is minimal. So we need to get the matrix for the normal ...
1
vote
1answer
23 views

Looking for a approximation/solution to my mortgage calculator function

I'm working on a little function, $t(A,y,r)$ that calculates the monthly payment of a fixed-rate mortgage, where $A$ is the amount borrowed, $y$ is the number of years over which the loan will be ...
0
votes
1answer
81 views

Rate of exponential decay

Good day all I have this curve (it is a solution of a partial differential equation that am working on) and I want to calculate numerically the rate of exponential decay but I don't know how to go ...
1
vote
1answer
38 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
142 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
145 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
128 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
719 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
94 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
322 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 ...