Questions on the arbitrary precision capabilities of Mathematica.

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44
votes
3answers
1k views

When I can assume that all decimal digits returned by Mathematica are provably correct?

How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: ...
25
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 ...
17
votes
1answer
607 views

Quadruple-precision (128 bit) arithmetic

Is it possible to force Mathematica to perform computations with hardware supported quadruple-precision? The following test suggest, that all of the computations with fixed precision, different than ...
15
votes
1answer
2k views

Global precision setting

Coming from Maple I do not understand how the precision for numerical computations in Mathematica is specified. I understand that there are various options to commands such as ...
13
votes
3answers
333 views

the winding number for the circle map (Arnold tongue)

I want to do an iterative calculation: f[n_, a_, b_] := Nest[# + a - b Sin[2 π #] &, 0, n]/n; If I use i use the machine precision, it maybe produce a great ...
12
votes
4answers
366 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 ...
12
votes
2answers
302 views

What determines the value of $MaxNumber?

What determines the value of $MaxNumber? $MaxNumber 1.233433712981650*10^323228458 ...
12
votes
2answers
221 views

Arbitrary precision spline interpolation

Current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang say here that "it is not hard to implement it ...
11
votes
1answer
976 views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
10
votes
3answers
513 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 ...
7
votes
2answers
297 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
3answers
266 views
6
votes
1answer
247 views

A problem with polynomial root finding

I use the expression ...
6
votes
0answers
455 views

Optimizing NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
5
votes
1answer
207 views

Accurately evaluating the hypergeometric function

As part of another problem, I am working to evaluate hypergeometric functions such as Hypergeometric2F1[1, 1, n, -1] for large $n$. I am hoping to obtain at ...
4
votes
1answer
558 views

How to set the working precision globally? $MinPrecision does not work

I want to increase the precision globally to 50 at least, but $MinPrecision does not work. ...
3
votes
1answer
379 views

Can some one explain perplexing behavior of arbitrary precision arithmetic?

I was exploring the problem presented by another question, when I ran into some behavior of Mathematica's arbitrary precision arithmetic engine that perplexes me. Here is what I was doing ...
3
votes
2answers
123 views

Why do I keep getting 0.06 with WorkingPrecision->1?

I'm trying to generate a list of 1000 random numbers with WorkingPrecision->1. Is there any particular reason that I'm getting some entries as 0.06? I have tested the following lines: ...
3
votes
1answer
117 views

NDSolve with varying PrecisionGoal and WorkingPrecision

Sometimes we need higher numerical precision to deal with large number cancellation in an equation. But if this cancellation happens only in a small (and known) parameter space, would it be possible ...
2
votes
4answers
124 views

Evaluating Erf[x] in arbitrary precision

Is it possible to evaluate Erf[200] with arbitrary precision? I only get 1. as result but I would like to know if a arbitrary ...
2
votes
1answer
361 views

Manipulating an arbitrary-precision ContourPlot

I have a function, say minimizeme[ω_][β_][ϵ_] = ϵ^2 ω-Log[2 (Cosh[2 β]+Cosh[2 β ϵ])]/(2 β); I want to make a high-precision dynamic ...
2
votes
1answer
160 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
1answer
182 views

Need more float precision

I have a Physics problem which huge and tiny numbers and Mathematica just gives me a speed of my particles which is the speed of light. Then $1/\sqrt{1-v^2/c^2}$ becomes singular. If I use smaller ...
2
votes
0answers
744 views

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 ...
1
vote
3answers
300 views

Making a calculation with high precision

I would like to make the following calculation: 1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1 Mathematica 8 returns 0. The result is obviously not 0, but my ...
1
vote
3answers
342 views

Setting the Accuracy of calculations

I am optimizing an equation that involves a number of trigonometric functions and Exp[]. How do I make sure that all my calculations have an accuracy of 120-200 ...
1
vote
1answer
474 views

Is LinearSolve the most robust way to solve the equation $Ax=b$?

I want to solve the equation $Ax=b$, where $A$ is an $n\times n$ matrix, and $x$ and $b$ are $n\times 1$ column vectors. Here $n=124$. LinearSolve[A,b] I got the ...
1
vote
1answer
355 views

How to increase precision: $MinPrecision does not help [duplicate]

I have the following series: ...
1
vote
1answer
84 views

How do I craft this constant to a specific accuracy?

An earlier post was migrated to Physics.SE and we determined that if this converged, we would have a constant close to the mass of the proton in kilograms. This constant is constructed by summing the ...
1
vote
0answers
180 views

Parallel linear algebra with arbitrary precision

Is it possible to do parallel linear algebra with arbitrary precision within Mathematica (in a simple manner, as is done for the machine precision)?
0
votes
1answer
590 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 ...
0
votes
1answer
62 views
0
votes
1answer
52 views

Error about limit MaxExtraPrecision

After my evaluations I have an error: N::meprec: Internal precision limit $MaxExtraPrecision=50. reached while evaluating ... ...
-1
votes
1answer
83 views

Verify factorization of RSA numbers [closed]

How would I verify the factorizations here with Mathematica? (read: multiply the two 100+ bit factors and check equality with the intended product).