# Questions tagged [machine-precision]

For questions on the use of machine-precision real numbers (also known as floats), the numbers that can be directly manipulated through the underlying numerical capabilities of your computer system.

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### Very different results from evaluating same expression with different precisions

When I evalute the following expression, ...
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### Finite precision - how to get rid of “near zeros” [duplicate]

I am performing a finite-precision operation on a matrix A which I know precisely; call the result B. The operation is taking ...
328 views

### Why is arithmetic faster for inexact arithmetic?

I have been trying to compute eigenvalues of a rather sizable matrix A, about $500 \times 500$ (but sparse). I asked Mathematica to compute ...
2k views

### Mathematica Precision

How can I set the output precision of the following statement to 10 decimal places? I was looking through the documentation, and for some reason, all I could find was ...
2k views

### Adding precision for the calculation of a function

I have some function $f(x)$ I wish to evaluate, which is yielding divide-by-zero errors for sufficiently large inputs. How do I increase the precision with which this function is evaluated in order ...
545 views

### Precision differences

I run this sum and get the symbolic answer below : Sum[ (1/(k^2 - k) - 1/k^2), {k, 2, Infinity}] $2 - \frac{\pi^2}{6}$ I look up the sequence on OEIS and ...
780 views

### How to Chop correctly?

I want to count degeneracies in a list called spectrum. The list contains numbers of double (~ 15digits) precision. So it makes no sense if the noise below this ...
1k views

### FindRoot errors

I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
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### Set Global Maximum Precision

I'm sure this has been asked before, but I've looked around and can't figure it out: How do I set a global maximum precision for a notebook (or in general, globally)? I have a large notebook in ...
3k views

### Precision of number not maintained when saved via Export

Assume that the output of my calculation is a and is a number such as: a = 100.1252135246354847; ...
719 views

### Could the PrecisionGoal for NDSolve be a negative number?

The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
857 views

### Mathematica Plot: Inconsistency when plotting large values

I am working with a function in Mathematica and I am getting some inconsistencies when I plot it. As I really need to understand were this comes from I would appreciate any help. I am working with a ...
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### Infinite expression 1/0. encountered - caused by precision?

Planck's law dependent on frequency rho is as follows: B[T_, h_, rho_, k_, c_] := (2 h rho^3)/c^2 1/(Exp[h rho/(T k)] - 1) As you can see, the denominator can ...