Questions on the arbitrary precision capabilities of Mathematica.

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49
votes
2answers
2k 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: ...
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 ...
25
votes
2answers
3k 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 ...
22
votes
4answers
824 views

Arbitrary precision spline interpolation

The current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang says here that "it is not hard to implement it ...
21
votes
7answers
716 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 ...
18
votes
1answer
839 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 ...
17
votes
4answers
599 views

the winding number for the circle map (Arnold tongue)

I want to perform an iterative calculation and visualize the results: f[n_, a_, b_] := Nest[# + a - b Sin[2 π #] &, 0, n]/n; If I use machine precision, it ...
17
votes
1answer
2k views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
12
votes
2answers
361 views

What determines the value of $MaxNumber?

What determines the value of $MaxNumber? $MaxNumber 1.233433712981650*10^323228458 ...
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 ...
8
votes
1answer
103 views

NDSolve`FiniteDifferenceDerivative gives wrong result when the precision is not MachinePrecision

Bug introduced in 8 or earlier and persists through 10.3.1 I want to get a pseudospectral differentiation matrix by NDSolve`FiniteDifferenceDerivative. ...
8
votes
1answer
104 views

Abnormal behavior of RealDigits[x]

In the Details of the document of RealDigits writes the following line: RealDigits[x] normally returns a list of digits of ...
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 ...
7
votes
3answers
381 views
7
votes
1answer
2k 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. ...
7
votes
1answer
367 views
6
votes
1answer
667 views

Preconditioning the objective function of NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
5
votes
1answer
330 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
620 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 ...
4
votes
1answer
125 views

Multidimensional arbitrary precision spline interpolation on the grid

This question is a generalization of the previous one for multiple dimensions. In the answer to that question an implementation for the clamped spline interpolation for 1D case and arbitrary degree of ...
3
votes
4answers
218 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 ...
3
votes
2answers
135 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
139 views

A difficult precision problem

I need to calculate values of a highly nonlinear recursive function, and I am confused by the results Mathematica is returning. ...
3
votes
1answer
51 views

Reals in Range; unexpected result for non-standard Precision

I think I have encountered advice against using inexact numbers in specifications of ranges and iterator many times. I don't think I ever saw an example of unexpected results though, but today I found ...
3
votes
1answer
271 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 ...
3
votes
1answer
134 views

How can I avoid these defects in ContourPlot3D output on WPC?

What I do: ContourPlot3D[-x^2/17.07 + y^2 + z^2 == 1 - x^17.07, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, Mesh -> None, PlotPoints -> 16] What I get: ...
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
1answer
557 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
217 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
1answer
78 views

Setting precision globally

This question is similar to this one and to this one. My code involves a lot of calls to Mathematica's N function, with the second argument (precision) set to 100 (say). I'm happy with the code, it ...
2
votes
1answer
95 views

Physical quantities to decimal power

How can I get Mathematica to properly simplify physical quantities with dimensions to decimal power, such as $1 \frac{1}{\text{s}^{0.7}}\text{dynes}\text{/(}\text{cm}^2\text{Pa})$ that should simplify ...
2
votes
0answers
1k 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
579 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
570 views

Setting the Accuracy of calculations

I need to optimize an expression that involves a number of trigonometric functions and Exp[]. How do I make sure that all my calculations have an accuracy of ...
1
vote
1answer
865 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
753 views

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

I have the following series: ...
1
vote
1answer
92 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
41 views

Diagonal times dense matrix, high precision

I have a fixed dense matrix M of high precision numbers, say 40 by 40 and precision 40. Then I have a variable vector v of the ...
1
vote
0answers
120 views

Ray tracing: Insufficient precision

I am writing a ray tracer to find the intersection point between a single ray and a cylinder. ...
1
vote
0answers
121 views

How to control precision of parameters in NonlinearModelFit?

I am using NonlinearModelFit for fitting a dataset to some complex numerical model function that depends on a few parameters. The final required precision of these parameters is very low, like 3 ...
1
vote
0answers
208 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
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 ...
0
votes
1answer
112 views
0
votes
1answer
178 views

Error about limit MaxExtraPrecision

After my evaluations I have an error: N::meprec: Internal precision limit $MaxExtraPrecision=50. reached while evaluating ... ...
0
votes
0answers
73 views

Can LinearSolve use Parallelize and WorkingPrecision in computation

I am looking for a two things while calculating the large array matrix equation: 1) To increase the precision in simple LinearSolve[] function 2) To find a way to parallelize the computation on all ...
0
votes
0answers
48 views

Failed to use SetPrecision

I am calculating the below formula: $$ \text{ER2}(\alpha,\text{K},\text{q})\text{:=}1+\sum _{m=0}^{K-1} \binom{K+\alpha }{m} \sum _{r=0}^m \frac{(-1)^r \binom{m}{r}}{\left(\frac{1}{q}\right)^{\alpha ...
-1
votes
1answer
157 views