Questions on the arbitrary precision capabilities of Mathematica.

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2answers
52 views

Mathematics arbitrary precision evaluation [duplicate]

I am trying to solve a simple expression: where a = 77617, and b = 33096. Wolfram|Alpha returns a correct result, using ...
1
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1answer
82 views

Why do these calculations 'stop'? [duplicate]

Question 1: If I change guess to a integer, for example guess = 1 then ListPlot already stops at $n=50$. This seems strange to me, any ideas on why this happens? ...
3
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1answer
138 views

Machine-Precision and Arbitrary Precision [closed]

What is meant by a machine number in the Mathematica documentation? What is the difference between machine-precision and fixed-point precision? What is arbitrary precision?
3
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1answer
60 views

MachinePrecision versus $MachinePrecision in NDSolve

I'd like to understand why one of these inputs gives me an error and the other doesn't: ...
0
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0answers
30 views

Analogue maple's Digits Environment Variable [duplicate]

I want setup (in Mathematica) once and for all operations number of digits after decimal point, similar how it's done in maxima: ...
16
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2answers
398 views

What determines the value of $MaxNumber?

What determines the value of $MaxNumber? $MaxNumber 1.233433712981650*10^323228458 ...
2
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1answer
82 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 ...
0
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2answers
77 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 +...
13
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2answers
185 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 ...
25
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2answers
4k 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 ...
9
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1answer
170 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
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1answer
150 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
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1answer
115 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 ...
5
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1answer
154 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 ...
6
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1answer
697 views
23
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3answers
991 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 ...
2
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1answer
104 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 ...
3
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1answer
140 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
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3answers
625 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 120-...
1
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0answers
132 views

Ray tracing: Insufficient precision

I am writing a ray tracer to find the intersection point between a single ray and a cylinder. ...
21
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7answers
788 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 ...
1
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0answers
48 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
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1answer
101 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 ...
3
votes
1answer
54 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
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4answers
247 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 ...
0
votes
0answers
113 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 ...
17
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4answers
683 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 ...
1
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0answers
166 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 ...
31
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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 ...
3
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1answer
334 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 ...
7
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1answer
3k 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. ...
0
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1answer
252 views

Error about limit MaxExtraPrecision

After my evaluations I have an error: N::meprec: Internal precision limit $MaxExtraPrecision=50. reached while evaluating ... ...
2
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1answer
274 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 ...
1
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1answer
995 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 ...
21
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1answer
2k views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
52
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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: machine-...
5
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1answer
371 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
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3answers
651 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
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1answer
914 views
0
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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
701 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
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0answers
213 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)?
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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
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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 ...