Questions tagged [arbitrary-precision]
Questions on the arbitrary precision capabilities of Mathematica.
146 questions
2
votes
1
answer
175
views
5
votes
2
answers
884
views
Strange results about the sine function of a big integer
I want to calculate the sine of a big integer, e.g., Sin[10^50], but found that N[Sin[10^50]], N[Sin[10^50],10], and N[Sin[10^50],20] give different results:
...
3
votes
2
answers
231
views
How does Mathematica compute the Precision of arithmetic calculations involving addition and multiplication of arbitrary precision numbers?
Consider the following simple calculation of the product of two 2x2 matrices composed of numerical values with specified precisions:
...
- 303
4
votes
1
answer
117
views
Dealing with mouse clicks in graphics objects that are beyond machine precision?
As a fun project with my kids, I've created a small GUI that enables us to explore the mandlebrot set. The GUI works great as long as you stay within machine precision. Even though the function <...
- 2,663
0
votes
0
answers
72
views
Underflow issue only by replacing the input variable of Exp with numbers
I was facing an underflow issue with Exp[]. I was able to fix that by following the suggestion: New General::munfl error and loss of precision
However, when the argument of Exp are variables and I try ...
- 23
4
votes
1
answer
216
views
Optimizing Iterative Computations with Large Ranges in Mathematica
I have an implementation in Mathematica that involves iteratively generating large ranges of values, performing element-wise operations, and calculating a cumulative product followed by a total. While ...
- 590
0
votes
0
answers
166
views
Optimizing a While Loop for High-Precision Computation in Mathematica
Edit: Clarifying the Core Issue
i=x;
While[Abs[p1 - p2] >= p1 tol,
p2 = p1;
p1 += s *= i (mkn + i)/((k1 - i) (n1 - i));
i--;
];
The core of my ...
- 590
2
votes
0
answers
102
views
Series, SeriesData, Approximate Numbers, and Precision Tracking [closed]
One of the features of Mathematica is the capability of doing arbitrary precision arithmetic and precision tracking. Mathematica has a build in command Series -- ...
2
votes
1
answer
148
views
Mapping Precision/Accuracy for Arbitrary-Precision Numbers to Significant Figures
(While there are similarities with my question here, this question deals with what Mathematica refers to as 'arbitrary precision numbers' and the former question deals with machine-precision numbers. ...
- 195
1
vote
2
answers
153
views
4
votes
1
answer
154
views
Plot freezes with arbitrary precision complex evaluations
I find that Plot has some strange behavior.
a = {{-5.355`3 I, 0.1589`3 }, {2.305`3, 0.01425`3}};
Det[a] // Abs
gives ...
- 295
2
votes
0
answers
113
views
NDSolve with integrated event, discrete variable and arbitrary-precision arithmetic gives error
I'm trying to solve an ODE numerically with NDSolve but get an unexpected error message (Experimental`NumericalFunction::nlnum1),...
- 103
0
votes
2
answers
162
views
Is there a way to convert a high precision value to its digits?
Is there a way to convert a number like 2.5326384172870370602159219766864657866396178797`20.124930050805514*^-12 to a high precision integer?
Mathematica gives me only 20 digits with ...
3
votes
4
answers
312
views
Calculating the angle between vectors returns small complex number instead of zero
I am calculating the angle between vectors
$$cos(\theta{_a}{_b}) = \frac{a^T b}{||a|| ||b||}$$
In mathematica I am coding
...
- 133
2
votes
2
answers
259
views
How to get correct numerical result without lots of digit precisions?
I am wondering if it is possible to get the correct numerical result without computing with a lot of precisions in expressions.
as a simple example suppose in the middle of some of my numerical code ...
2
votes
2
answers
319
views
How to prevent Mathematica from rounding some PDF values to 0?
Dear Mathematica community,
I'm having a problem with the PDF function for the hypoexponential distribution. Specifically, Mathematica returns 0 as soon as the value is very small. Below is an example:...
- 31
0
votes
1
answer
102
views
ToString[SetPrecision[x,1.2]] doesn't work as expected
2nd Code Block demonstrates failure in comment of output
...
0
votes
0
answers
67
views
Issues with ConvexOptimization and SetPrecision
I am completely new to Mathematica (second day), so do not expect things to look polished.
I am trying to perform a ConvexOptimization over a List/Array (dimensionality ...
- 113
0
votes
1
answer
142
views
Confusion about precision [duplicate]
When I evaluate
x = 1.0000000000000000001 (* Precision of 20 digits *)
Mathematica returns
...
- 1,783
-3
votes
1
answer
151
views
long division acurate answer on dividing long numbers [closed]
ok but first of all if i have the huge number to be divided what will i have to use for the division to be accurate long division or some other formula square root or 2 this is to calculate music ...
1
vote
0
answers
90
views
Finding the position of maximal value when dealing with precision numbers [closed]
In for example this answer a solution is given to find the position of a maximal value. However, this solutions seems to run into trouble when dealing with precision numbers. Take the following ...
- 4,931
2
votes
0
answers
152
views
Rational numbers in NDSolve
Is it possible to use NDSolve with Rational numbers instead of Real?
I use all rational ...
- 141
6
votes
2
answers
2k
views
How to force Mathematica to do infinite-precision calculations?
Consider the following calculation:
1234*5678*90.12
The result is:
6.31439*10^8
However, I want to get a precise result. Of ...
- 145
3
votes
1
answer
132
views
Precision in Graph methods
It appears that GraphDistance, GraphDistanceMatrix, FindShortestPath, etc. all work with ...
- 701
0
votes
0
answers
194
views
How to use Equal for close arbitrary precision numbers to be considered the same?
I am trying to add a comparator function in a larger piece of code which can equate two arbitrary precision numbers and yields True if they are approximately close.
...
- 9,130
1
vote
1
answer
217
views
General:munfl error problem
I have the following function, that is the result of The integration between x and some upper limit of a positive function, thus should be positive
$f(x,vE) = \frac{e^{-1140.09 x} \left(e^{67945.5 \...
- 419
3
votes
0
answers
381
views
How to deal with too small numbers
When dealing with a code that produces too small numbers (in a complicated way) like
0.33691 4.015757066049965*10^-330
I get the following warning
General::munfl: ...
- 399
1
vote
1
answer
155
views
2
votes
2
answers
387
views
Most efficient strategy for integrating over removable poles?
I am finding many situations where I have to numerically integrate some function $f(x)$ of the form:
$$f(x)=f_{s}(x)-ax^{-n},$$
where $f_s$ is a special function with a finite-order pole that is ...
- 1,120
2
votes
1
answer
336
views
Shouldn't NIntegrate return a number whose Precision is PrecisionGoal, not WorkingPrecision?
I know that Mathematica has great built-in precision tracking, so when you do calculations with arbitrary-precision numbers, Mathematica keeps track of the precision on the result. Given this careful ...
- 1,120
0
votes
0
answers
103
views
Use Check in a While loop without wasting the calculation
I am trying to generate and solve a matrix that tends towards being singular using variable arbitrary precision to ensure accuracy. Consider, for example, a matrix with tunable singularity:
...
- 7,609
0
votes
1
answer
133
views
Solving linear systems efficiently
In certain calculation I encountered a system of linear equations in 144 variables, and it takes hours to compute. Most probably the reason is that coefficients are really huge integers (about $10^{50}...
- 2,459
2
votes
1
answer
229
views
Difficulty when trying to find roots to high accuracy
I'm working with the logistic map $f(x,\lambda)=4\lambda x(1-x)$, and iterations of the logistic map $f^{(2^n)}(x,\lambda)=f^{(2^{n-1})}(f^{(2^{n-1})}(x,\lambda),\lambda)$. There are some special ...
- 270
1
vote
4
answers
369
views
Can I change the default behavior so that "0.1" is interpreted as "1/10" automatically?
Consider the function
f[a_] := NIntegrate[Sqrt[a + Log[x]], {x, 1, 10}, WorkingPrecision -> 30].
With this definition, I cannot call ...
- 1,120
0
votes
0
answers
92
views
Increase precision of ConvexHullMesh
I want to generate a set of equations for all planes in the convex hull as specified in this question. The problem is that the generated set of equations don't correctly cover all the points. I run a ...
- 133
1
vote
0
answers
215
views
FindMaximum does not use requested WorkingPrecision
I think that there is a bug in the way FindMaximum handles WorkingPrecision for constrained problems.
Has anyone encountered a similar problem before? Is there a work around?
Here is an example in ...
- 31
2
votes
0
answers
254
views
`LinearSolve` in arbitrary precision has a sudden change in performance as the size of a problem is gradually increased
It is expected that calculations in arbitrary precision are much slower than in machine precision. However, LinearSolve has an unexpected behavior: there is a ...
- 1,652
1
vote
2
answers
247
views
Does SetPrecision[x, Infinity] expose the internal exact number in the approximated number?
What I already know (maybe) :
My theory about Mathematica's way of implementing approximated number
An number approX with arbitrary precision ...
- 177
0
votes
1
answer
142
views
How to initialize arbitrary precision?
How do I calculate $$\frac{1}{{\frac{1}{7 \times 10^7}- \frac{8\times10^{17}\times 3.1\times 10^7}{6.7 \times 10^{-11}\times \left(1.9 \times 10^{27}\right)^2} }}\tag{1}$$
To arbitrary precision?
I ...
- 127
0
votes
0
answers
105
views
Creating an interpolation matrix efficiently
I would like to know if there is a fast way to create the following matrix (note that the matrix is defined with arbitrary precision):
...
- 627
2
votes
1
answer
159
views
Dealing with zero at high precision
I am using mathematica to deal with rational functions, $p(x)/q(x)$, where the polynomials, $p,q$ have a high degree and coefficients with high order of precision, e.g:
...
- 341
2
votes
0
answers
58
views
Set Underflow precision in Mathematica 12 same as version 11.x [duplicate]
It seems like Mathematica version 12 sets arbitrary underflow precision depending on the function, but I would like the underflow precision to be same as what was for previous version of Mathematica ...
- 631
0
votes
0
answers
75
views
What is the limit of digits to show in the conversion of an exact number to an Arbitrary Precision Number?
By executing something like N[π, c] what is the maximum positive integer value c can have until the output is compromised by ...
- 41
4
votes
0
answers
174
views
How does Mathematica evaluate N[π, 30] == π? [closed]
I want to know how N[π, 30] == π works. The result is True. I wonder whether the exact number ...
- 41
6
votes
1
answer
281
views
Linear Algebra in Arbitrary Precision - SLOW
I am trying to implement an arbitrary precision algorithm, but I am not very familiar with Mathematica or arbitrary precision arithmetic. I was able to implement it but surprised by how much slower it ...
- 81
2
votes
0
answers
116
views
Changing machine precision notebook-wide leads to peculiarities
For a project of mine it is preferrable to set notebook precision globally. I have done so by using the answer in Global precision setting.
The idea is to dynamically create a ...
- 317
0
votes
1
answer
140
views
Why this very simple problem turns to "Indeterminate"?
Why the following calculation gives Indeterminate value?
...
- 639
0
votes
1
answer
199
views
Preventing Mathematica from considering small values to be equal to zero [duplicate]
In my calculations I have a variable (say z) which can be an argument of Log, say, z Log[z]. ...
- 639
1
vote
1
answer
147
views
Number definition and approximation
I run these lines:
a = 0.833
SetPrecision[a, 20]
and this is the output:
0.833
0.83299999999999996270
I expected to ...
- 103
7
votes
1
answer
136
views
DumpSave and precision of interpolation data
Consider the following
prec = 32;
x = N[Range[0, 1, 1/10], prec];
f = Interpolation[Transpose@{x, x}];
Then
...
- 3,558