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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28
votes
2answers
1k views

Meaning of backtick in floating-point literal

If I compute, say, 1/3//N, Mathematica displays 0.333333 as the result. When I copy that output to use elsewhere, the paste ...
11
votes
2answers
541 views
8
votes
2answers
449 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 ...
8
votes
1answer
376 views

DeleteDuplicates[] does not work as expected on floating point values

Here is my simple example, and in this case function DeleteDuplicates does not work as expected. I want to FindRoot of my ...
25
votes
1answer
629 views

Is there a difference between Divide[a,b] and a/b?

In this comment it was asserted that Divide[a,b] and a/b are different, though the documentation indicates that they are the ...
15
votes
4answers
2k views

Numerical underflow for a scaled error function

I calculate scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ...
21
votes
7answers
717 views

Elegant high precision `log1p`?

Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ...
10
votes
1answer
173 views

Compilation of Total with compensated summation

I sometimes obtain an unexpected error when trying to call a compiled version of Total with compensated summation turned on. More specifically I define ...
7
votes
3answers
381 views
10
votes
3answers
711 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 ...
3
votes
2answers
298 views

How to make the computer consider two numbers equal up to a certain precision

My problem is that I have a matrix A and the computer says is not Hermitian (self-adjoint). Then I check which elements make A ...
3
votes
2answers
979 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; ...
1
vote
1answer
195 views

How to increase significant digits in Mathematica

How can I increase the number of significant digits in Mathematica? When I import a matrix, an element like 112.5276 is rounded to 112.528. I would like to increase the number of significant digits ...
0
votes
2answers
139 views

The precision of the number

I have problem in Mathematica with unnecessary rounding which is caused by high precision. For example I have value a = 2.052685846*10^-1865, when I make ...
6
votes
4answers
1k 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 ...
0
votes
1answer
1k 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 ...
5
votes
1answer
93 views

Compilation, square roots, and integers

After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ...
5
votes
1answer
74 views

Can Someone Please Explain Internal`$SameQTolerance?

If I input Internal`$SameQTolerance (* output = 0.30103 *) which is the approximation of Log[10,2], or ...
3
votes
1answer
216 views

Why to do parentheses change the results of a calculation?

I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2 ...
7
votes
1answer
143 views

Using Differences on data: trouble with floats and doubles

Consider the following data set (after I have run FullForm), which is imported from a file (stored typically as 10.040): ...
7
votes
2answers
368 views

Dealing with numbers too large for machine precision in Graphics

Graphics only supports machine precision numbers (i.e. number that can be converted to machine precision). Take for example ...
6
votes
1answer
120 views

Issues with $MachineEpsilon

I'm attempting to add $MachineEpsilon to numbers I am pulling from the domains of 3 interpolating functions. I pulled 3 numbers, and for one of these numbers adding ...
3
votes
1answer
401 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 ...
2
votes
1answer
248 views

How to use adaptive precision in matrix computations?

I wish to compute the pseudo inverse of rectangular (or square) matrices by the cubically method of Chebyshev given by $X_{k+1}=X_k(3I-AX_k(3I-AX_k))$ where $X_0=\frac{1}{\|A\|_F^2}A^*$. The procedure ...
2
votes
2answers
605 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 ...
1
vote
0answers
68 views

Floor inconsistent with Less for machine-precision approximate numbers

For machine-precision numbers, Mathematica uses a tolerance for comparisons, so that 1.-$MachineEpsilon==1. However, Floor does ...
1
vote
1answer
142 views

Why does it matter at what point I replace?

I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points. I use (LK4 is defined below, but its shape should have nothing to do with my ...
0
votes
1answer
92 views

Floating point arithmetic bug caused by Table[]

I was doing something fairly ordinary and noticed something I can't, for the life of me, explain. For context, I wanted to take make a function that takes an array of data like the one below, then an ...
0
votes
1answer
998 views

How to change machineprecision digits

I am trying to compute t0: ...