Questions tagged [arbitrary-precision]

Questions on the arbitrary precision capabilities of Mathematica.

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39
votes
2answers
3k 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 ...
29
votes
3answers
3k 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 ...
66
votes
3answers
3k views

When can I 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-...
36
votes
3answers
9k 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
votes
3answers
1k views

Very different results from evaluating same expression with different precisions

When I evalute the following expression, ...
30
votes
8answers
1k 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 ...
39
votes
1answer
4k views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
20
votes
2answers
2k views

How are Accuracy and Precision related Mathematica for a given operation?

The common understanding for Accuracy and Precision in English language is given by this figure. Inspired by this question I have a follow up question relating ...
6
votes
1answer
676 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?
17
votes
1answer
10k 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. ...
10
votes
3answers
871 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 ...
9
votes
1answer
195 views

Plot3D discrepancy between MMA 10 and 11.3 - possible small numbers issue

I'm having some troubles with the following code I wrote in MMA 10 some time ago: ...
7
votes
1answer
313 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
votes
4answers
2k 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 ...
4
votes
1answer
243 views

How to disable roundoff error tracking in arbitrary precision arithmetic?

In my calculations I need some larger precision. But due to the fact that I iteratively refine the results to compensate for rounding errors accumulated in previous iteration, Mathematica's arbitraty ...
2
votes
1answer
1k 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 ...
4
votes
1answer
417 views

WorkingPrecision in NDSolve causes failure when solving a simple PDE

I have fivefold multiple integral and I wanted a speed calculations. I came across on this Question and had already begun the problems. Here is a toy example with simple double integral: ...
1
vote
1answer
264 views

Why does Fourier give a large error in MachinePrecision?

Consider this code: ...
0
votes
1answer
72 views

Why this very simple problem turns to “Indeterminate”?

Why the following calculation gives Indeterminate value? ...
19
votes
2answers
868 views

Error and uncertainty propagation: Is using Precision/Accuracy a sound strategy?

Questions What are the available resources to deal with experimental error and uncertainty propagation in Mathematica? Given that Mathematica already uses linearized model of error propagation on ...
7
votes
1answer
710 views

Really understanding precision

I've been reading the documentation in Mathematica about precision, namely: Exact and Approximate Results Arbitrary-Precision Numbers Arbitrary-Precision Calculations Machine-Precision Numbers ...
27
votes
3answers
722 views

What determines the value of $MaxNumber?

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

Arbitrary-Precision Arithmetic behaves unexpectedly

I want to understand how small numerical errors propagate through a computation and may drastically change the final result. To this end, I consider a toy world in which every number is limited to ...
1
vote
1answer
2k 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 ...
8
votes
2answers
469 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
4answers
385 views

How do I convert an inexact number smaller than $MinMachineNumber to machine-precision?

I was trying to convert some arbitrary-precision numbers to machine-precision numbers using N[myNumber,MachinePrecision]. But, although my test number did lose some ...
4
votes
1answer
330 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: ...
1
vote
2answers
121 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 ...
11
votes
1answer
135 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 ...
9
votes
1answer
178 views

Has “faster arbitrary precision computation of elementary functions” been incorporated into Mathematica?

In this Wolfram Conference talk from last year, "Faster Arbitrary Precision Computation of Elementary Functions", they talk about R&D for algorithms to numerically evaluate elementary functions ...
6
votes
2answers
221 views

$N[a,50]-N[a,10]=0$ why? and what's the rationale behind?

Let $a=\sqrt{3}$. What's the point of having In[102]:= N[Sqrt[3],100]-N[Sqrt[3],10] Out[102]= 0.*10^-10 ? Let's imagine I wanted to get the difference between ...
5
votes
2answers
184 views

Early vs. late application of arbitrary precision

The following arbitrary-precision computations, in which arbitrary precision is applied early (to the inputs), both work as expected: ...
2
votes
1answer
2k 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 ...
2
votes
1answer
454 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
vote
1answer
148 views

Interpolation function precision in multi dimentional case

I have this interpolation example ...
1
vote
2answers
197 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 +...
0
votes
1answer
230 views

Mathematica will not run Arnoldi method while using NIntegrate

This is simplified version of my real code: ...