# Tagged Questions

Questions on the arbitrary precision capabilities of Mathematica.

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### 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 ...
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? ...
145 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?
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### Mathematica will not run Arnoldi method while using NIntegrate

This is simplified version of my real code: ...
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### MachinePrecision versus $MachinePrecision in NDSolve I'd like to understand why one of these inputs gives me an error and the other doesn't: ... 0answers 30 views ### Analogue maple's Digits Environment Variable [duplicate] I want setup (in Mathematica) once and for all operations number of digits after decimal point, similar how it's done in maxima: ... 2answers 398 views ### What determines the value of$MaxNumber?

What determines the value of $MaxNumber?$MaxNumber 1.233433712981650*10^323228458 ...
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 ...
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### 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 +...
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### 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 ...
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 ...
172 views

### NDSolveFiniteDifferenceDerivative 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 NDSolveFiniteDifferenceDerivative. ...
152 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. ...
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 ...
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 ...
697 views

### Preconditioning the objective function of NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
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 ...
109 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 ...
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: ...
391 views

### A problem with polynomial root finding

I use the expression ...
626 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-...
132 views

### Ray tracing: Insufficient precision

I am writing a ray tracer to find the intersection point between a single ray and a cylinder. ...
792 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
187 views

### How do I find my maximum precision on my computer? [duplicate]

I'm trying to run this ...
685 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 ...
168 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 ...
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### Changing working precision to 10 in NIntegrate introducing error messages and giving bigger error than precision 5

I have two numerical integrals as follows: ...
132 views

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

Consider this code: ...
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 ...
335 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 ...
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After my evaluations I have an error: N::meprec: Internal precision limit $MaxExtraPrecision=50. reached while evaluating ... ... 1answer 275 views ### How to use adaptive precision in matrix computations? I wish to compute the pseudo inverse of rectangular (or square) matrices by the cubically method of Chebyshev given by$X_{k+1}=X_k(3I-AX_k(3I-AX_k))$where$X_0=\frac{1}{\|A\|_F^2}A^*$. The procedure ... 1answer 999 views ### Is LinearSolve the most robust way to solve the equation$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$. LinearSolve[A,b] I got the ... 3answers 430 views ### Very different results from evaluating same expression with different precisions When I evalute the following expression, ... 1answer 2k views ### AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ... 2answers 2k views ### When I can assume that all decimal digits returned by Mathematica are provably correct? How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: machine-... 1answer 373 views ### Accurately evaluating the hypergeometric function As part of another problem, I am working to evaluate hypergeometric functions such as Hypergeometric2F1[1, 1, n, -1] for large$n$. I am hoping to obtain at ... 3answers 654 views ### Making a calculation with high precision I would like to make the following calculation: 1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1 Mathematica 8 returns 0. The result is obviously not 0, but my ... 1answer 919 views ### How to increase precision:$MinPrecision does not help [duplicate]

I have the following series: ...
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### 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 ...
704 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 ...
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### 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)?