# Questions tagged [arbitrary-precision]

Questions on the arbitrary precision capabilities of Mathematica.

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### 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 ...
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 ...
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-...
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 ...
1k views

### Very different results from evaluating same expression with different precisions

When I evalute the following expression, ...
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 ...
4k views

### AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
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 ...
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?
10k views

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### 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 ...
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: ...
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 ...
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 ...
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 ...
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### 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 ...
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: ...
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### Why does Fourier give a large error in MachinePrecision?

Consider this code: ...
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### Why this very simple problem turns to “Indeterminate”?

Why the following calculation gives Indeterminate value? ...
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 ...
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 ...
722 views

### What determines the value of $MaxNumber? What determines the value of$MaxNumber? $MaxNumber 1.233433712981650*10^323228458 ... 1answer 209 views ### Arbitrary-Precision Arithmetic behaves unexpectedly I want to understand how small numerical errors propagate through a computation and may drastically change the final result. To this end, I consider a toy world in which every number is limited to ... 1answer 2k views ### Adding precision for the calculation of a function I have some function$f(x)$I wish to evaluate, which is yielding divide-by-zero errors for sufficiently large inputs. How do I increase the precision with which this function is evaluated in order ... 2answers 469 views ### Dealing with numbers too large for machine precision in Graphics Graphics only supports machine precision numbers (i.e. number that can be converted to machine precision). Take for example ... 4answers 385 views ### How do I convert an inexact number smaller than$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 ...