# Tagged Questions

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 ...
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 ...
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### 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 ...
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 ...
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 ...
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 ...
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 ...