Questions on the arbitrary precision capabilities of Mathematica.

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2
votes
1answer
64 views

How to tell Mathematica to treat all numbers (including those in decimal form) as arbitrary precision numbers

I have code that is essentially numerical. It uses functions like NDSolve and NIntegrate. But in most interesting cases, the ...
8
votes
1answer
140 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. ...
4
votes
1answer
145 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. ...
11
votes
1answer
114 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 ...
2
votes
1answer
91 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 ...
12
votes
2answers
178 views

What is the best way to transfer arbitrary-precision reals using WSTP?

I'm developing a Mathematica package, inside of which there is a number-crunching function. It uses a list of arbitrary-precision numbers as input and it takes a lot of time to do its job. So I've ...
3
votes
1answer
136 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: ...
1
vote
0answers
46 views

Diagonal times dense matrix, high precision [closed]

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 ...
2
votes
1answer
97 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 ...
5
votes
1answer
145 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
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 ...
0
votes
0answers
94 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 ...
-1
votes
1answer
171 views
1
vote
0answers
125 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
141 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 ...
0
votes
2answers
73 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 ...
17
votes
4answers
642 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 ...
0
votes
1answer
121 views
3
votes
4answers
232 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
1answer
308 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 ...
0
votes
1answer
219 views

Error about limit MaxExtraPrecision

After my evaluations I have an error: N::meprec: Internal precision limit $MaxExtraPrecision=50. reached while evaluating ... ...
23
votes
4answers
914 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
745 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 ...
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. ...
1
vote
1answer
928 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 ...
7
votes
3answers
405 views
7
votes
1answer
376 views
2
votes
1answer
257 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 ...
50
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: ...
5
votes
1answer
339 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 ...
1
vote
3answers
610 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
1answer
832 views

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

I have the following series: ...
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 ...
4
votes
1answer
658 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 ...
1
vote
0answers
209 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)?
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 ...
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 ...
18
votes
1answer
2k views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
6
votes
1answer
683 views

Preconditioning the objective function of NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
2
votes
1answer
605 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 ...
1
vote
3answers
599 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 ...
10
votes
3answers
727 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
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: ...
2
votes
1answer
219 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 ...
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 ...
18
votes
1answer
864 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 ...
7
votes
2answers
375 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 ...
28
votes
2answers
2k 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 ...
14
votes
2answers
368 views

What determines the value of $MaxNumber?

What determines the value of $MaxNumber? $MaxNumber 1.233433712981650*10^323228458 ...