# Tagged Questions

Questions on the arbitrary precision capabilities of Mathematica.

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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: ...
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### Verify factorization of RSA numbers [closed]

How would I verify the factorizations here with Mathematica? (read: multiply the two 100+ bit factors and check equality with the intended product).
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### the winding number for the circle map (Arnold tongue)

I want to do an iterative calculation: f[n_, a_, b_] := Nest[# + a - b Sin[2 π #] &, 0, n]/n; If I use i use the machine precision, it maybe produce a great ...
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### Why does Fourier give a large error in MachinePrecision?

Consider this code: ...
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### 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 ...
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### 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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I want to increase the precision globally to 50 at least, but $MinPrecision does not work. ... 1answer 509 views ### Is LinearSolve the most robust way to solve the equation$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$. LinearSolve[A,b] I got the ... 3answers 269 views ### Very different results from evaluating same expression with different precisions When I evalute the following expression, ... 1answer 256 views ### A problem with polynomial root finding I use the expression ... 1answer 166 views ### How to use adaptive precision in matrix computations? I wish to compute the pseudo inverse of rectangular (or square) matrices by the cubically method of Chebyshev given by$X_{k+1}=X_k(3I-AX_k(3I-AX_k))$where$X_0=\frac{1}{\|A\|_F^2}A^*$. The procedure ... 3answers 1k views ### When I can assume that all decimal digits returned by Mathematica are provably correct? How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: ... 1answer 209 views ### Accurately evaluating the hypergeometric function As part of another problem, I am working to evaluate hypergeometric functions such as Hypergeometric2F1[1, 1, n, -1] for large$n$. I am hoping to obtain at ... 3answers 323 views ### Making a calculation with high precision I would like to make the following calculation: 1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1 Mathematica 8 returns 0. The result is obviously not 0, but my ... 1answer 382 views ### How to increase precision:$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 ...
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### 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)?
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### 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 ...
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### 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 ...
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### AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
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### Optimizing NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
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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 ...
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### Setting the Accuracy of calculations

I am optimizing an equation that involves a number of trigonometric functions and Exp[]. How do I make sure that all my calculations have an accuracy of 120-200 ...
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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 ...
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### 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: ...
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### 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 ...
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### 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 ...
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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 ...
306 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 ...