# Questions tagged [arbitrary-precision]

Questions on the arbitrary precision capabilities of Mathematica.

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### InverseFunction: Precision problem

I define a function SS[t] as an inverse function: ...
2answers
90 views

### Most efficient strategy for integrating over removable poles?

I am finding many situations where I have to numerically integrate some function $f(x)$ of the form: $$f(x)=f_{s}(x)-ax^{-n},$$ where $f_s$ is a special function with a finite-order pole that is ...
1answer
78 views

### Shouldn't NIntegrate return a number whose Precision is PrecisionGoal, not WorkingPrecision?

I know that Mathematica has great built-in precision tracking, so when you do calculations with arbitrary-precision numbers, Mathematica keeps track of the precision on the result. Given this careful ...
0answers
49 views

### Use Check in a While loop without wasting the calculation

I am trying to generate and solve a matrix that tends towards being singular using variable arbitrary precision to ensure accuracy. Consider, for example, a matrix with tunable singularity: ...
0answers
31 views

### How to avoid machine underflow for plotting and integrating?

I am trying to integrate the following integrand, which I have plotted: ...
1answer
60 views

In certain calculation I encountered a system of linear equations in 144 variables, and it takes hours to compute. Most probably the reason is that coefficients are really huge integers (about $10^{50}... 1answer 83 views ### Difficulty when trying to find roots to high accuracy I'm working with the logistic map$f(x,\lambda)=4\lambda x(1-x)$, and iterations of the logistic map$f^{(2^n)}(x,\lambda)=f^{(2^{n-1})}(f^{(2^{n-1})}(x,\lambda),\lambda)$. There are some special ... 4answers 142 views ### Can I change the default behavior so that “0.1” is interpreted as “1/10” automatically? Consider the function f[a_] := NIntegrate[Sqrt[a + Log[x]], {x, 1, 10}, WorkingPrecision -> 30]. With this definition, I cannot call ... 0answers 38 views ### Increase precision of ConvexHullMesh I want to generate a set of equations for all planes in the convex hull as specified in this question. The problem is that the generated set of equations don't correctly cover all the points. I run a ... 0answers 100 views ### FindMaximum does not use requested WorkingPrecision I think that there is a bug in the way FindMaximum handles WorkingPrecision for constrained problems. Has anyone encountered a similar problem before? Is there a work around? Here is an example in ... 0answers 39 views ### LinearSolve in arbitrary precision has a sudden change in performance as the size of a problem is gradually increased It is expected that calculations in arbitrary precision are much slower than in machine precision. However, LinearSolve has an unexpected behavior: there is a ... 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 ... 1answer 43 views ### How to initialize arbitrary precision? How do I calculate $$\frac{1}{{\frac{1}{7 \times 10^7}- \frac{8\times10^{17}\times 3.1\times 10^7}{6.7 \times 10^{-11}\times \left(1.9 \times 10^{27}\right)^2} }}\tag{1}$$ To arbitrary precision? I ... 0answers 63 views ### Creating an interpolation matrix efficiently I would like to know if there is a fast way to create the following matrix (note that the matrix is defined with arbitrary precision): ... 1answer 69 views ### Dealing with zero at high precision I am using mathematica to deal with rational functions,$p(x)/q(x)$, where the polynomials,$p,q$have a high degree and coefficients with high order of precision, e.g: ... 0answers 43 views ### Set Underflow precision in Mathematica 12 same as version 11.x [duplicate] It seems like Mathematica version 12 sets arbitrary underflow precision depending on the function, but I would like the underflow precision to be same as what was for previous version of Mathematica ... 0answers 42 views ### What is the limit of digits to show in the conversion of an exact number to an Arbitrary Precision Number? By executing something like N[π, c] what is the maximum positive integer value c can have until the output is compromised by ... 0answers 126 views ### How does Mathematica evaluate N[π, 30] == π? I want to know how N[π, 30] == π works. The result is True. I wonder whether the exact number ... 1answer 114 views ### Linear Algebra in Arbitrary Precision - SLOW I am trying to implement an arbitrary precision algorithm, but I am not very familiar with Mathematica or arbitrary precision arithmetic. I was able to implement it but surprised by how much slower it ... 0answers 37 views ### Changing machine precision notebook-wide leads to peculiarities For a project of mine it is preferrable to set notebook precision globally. I have done so by using the answer in Global precision setting. The idea is to dynamically create a ... 1answer 72 views ### Why this very simple problem turns to “Indeterminate”? Why the following calculation gives Indeterminate value? ... 1answer 68 views ### Preventing Mathematica from considering small values to be equal to zero [duplicate] In my calculations I have a variable (say z) which can be an argument of Log, say, z Log[z]. ... 1answer 88 views ### Number definition and approximation I run these lines: a = 0.833 SetPrecision[a, 20] and this is the output: 0.833 0.83299999999999996270 I expected to ... 0answers 51 views ### DumpSave and precision of interpolation data Consider the following prec = 32; x = N[Range[0, 1, 1/10], prec]; f = Interpolation[Transpose@{x, x}]; Then ... 1answer 314 views ### How can I suppress the warning “precision may be lost”? When I import data from a .dat file, V11.3 emits the message: is too small to represent as a normalized machine number; precision may be lost. How can I close the ... 2answers 922 views ### Truncate a number in mathematica I want to truncate a simple number to n decimal digits. For example, 2/3. I used f[x_, n_] := N[IntegerPart[x 10^n]/10^n] but I get ... 1answer 56 views ### How to get the correct result in a simple operation in Mathematica I have the following values for x[[i]], y[[i]] and A[[i,j]]: ... 1answer 56 views ### Simple division with high precision in Mathematica [closed] I want to do a simple division i.e. 0.70524/0.51824 . What I want is to find the result of the roundation of this division for precision from 1 to 19 decimal digits.... 0answers 136 views ### Arbitrary Precision, Nearly-Singular Matrices, and LinearSolve I have been trying to solve a nonlinear eigenvalue problem,$\mathbf{M}(\lambda) \mathbf{v} = 0$, in Mathematica using Newton's method. The core of the algorithm relies upon an inverse iteration, ... 2answers 427 views ### Why does N not upgrade precision? [duplicate] Precision[N[1.0, 20]] Precision[N[1, 20]] MachinePrecision 20. It would be so much more intuitive and less error prone, if <... 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: ... 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: ... 1answer 697 views ### What is wrong with importing Real32 or Real64? Those who visit the chat might have seen the question of varkor. I'm posting it here in the hope that I have missed something. Assume you have a real number ... 1answer 259 views ### Mathematica precision common problems When I do something a little bit more complicated than standard documentation examples, I often hit precision problem. Or I accidentally disprove Riemann hypothesis Like this ... 1answer 149 views ### Interpolation function precision in multi dimentional case I have this interpolation example ... 1answer 236 views ### Can NDEigensystem use arbitrary precision arithmetic? Consider the following computation of an eigenfunction of 1D Laplacian on the interval of$[0,\pi]$: ... 2answers 2k views ### Fast integer square-root I'm looking for the highest-performance method of calculating integer square roots in Mathematica of very big arbitrary-precision numbers. As an example testcase, I use: ... 1answer 169 views ### plot of polynomial expression failed [duplicate] I want to plot a polynomial expression for {a,0,1}: ... 1answer 91 views ### Rigorous error bounds for NIntegrate Suppose I want to numerically evaluate an integral of the form $$\int_{-\infty} ^\infty f(x) \mathrm{d}x$$ with error not exceeding some positive bound$\epsilon$. Is there a way to do this using <... 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 ...
0answers
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### Arbitrary precision calculation makes my computer hang

I have this code list = Accumulate@Tan[N[Range[10^8]]]; // AbsoluteTiming and the timing is slightly more than two seconds. Now if I try to compute this ...
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 ...
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 ...
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 ...
1answer
82 views

### Simple precision issue [closed]

Considering binomial expansion $1 = (p+(1-p))^n = \sum_{k=0}^n p^n (1-p)^{n-k},$ which is true for any real value of $p$, I'm getting diverging results when I numerically evaluate the above even ...
1answer
65 views

### Constructing a List from a Decimal Number

I am trying to get from a number such as $12.345$ to a list $\{1,2,3,4,5\}$. My best attempt so far has been: First[RealDigits[12.345]] however this of course ...
0answers
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2answers
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### Why does SetPrecision not apply to 0?

Is there a rationale why SetPrecision works on integers except for 0? SetPrecision[1,5] 1.0000 ...
1answer
771 views

### Why does 1 - Exp[-10.0^12] cause an out-of-memory error?

I would like to understand why evaluation of the expression 1 - Exp[-10.0^12] causes an out-of-memory error and how can I prevent such errors when calculating ...
1answer
81 views

### Why does SetPrecision drop “unknown” digits if precision requested is Infinity but retain them if it's finite?

I was trying to reset the imprecision record of a number like 0.0076022266122755632`1.025 by calling SetPrecision with second ...