# Questions tagged [machine-precision]

For questions on the use of machine-precision real numbers (also known as floats), the numbers that can be directly manipulated through the underlying numerical capabilities of your computer system.

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### Indeterminant numerical value of summation

I have the following two-fold summation. ...
• 1,122
141 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]. ...
• 629
77 views

### ContourPlot showing breaks in contours

I'm trying find graphically the solutions of the intersection of the following functions. ...
• 573
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### 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]]: ...
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### NIntegrate numerical accuracy and errors

I have the following 3x3 matrix M = {{-I*ω + Γ/2, I*g1, 0}, {I*g1, -I*ω + κ1/2, I*g2}, {0, I*g2, -I*ω + κ2/2}}; Finding the eigenvalues and eigenvectors ...
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### How to use a higher precision?

Below is my code. If I set W to $10^{55}$, it breaks down and the result is wrong. What do I need to do to use W as large as $10^{200}$? ...
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### How to improve the performance of this code

I have implemented a code in Mathematica 9 to simulate a scattering problem, and I got really disappointed about its performance when compared to Matlab. Since I am a newbie in Mathematica, would ...
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### How to set the precision for the entire notebook

I want to do various computations conditional on a given precision for the entire notebook. I use the following code: ...
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### When does arithmetic with approximate numbers not follow basic properties? [closed]

Consider this: x = Exp[3.5*^15] (* OVerflow[] *) The above is well documented and so is the next result. ...
• 884
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### Overflow + Underflow Problems with Code

I am trying to use Mathematica to verify simulation results with an analytic result. The analytic results are performance measures of the M/D/1 queue, which unfortunately uses the factorial function ...
• 427
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### How to set up precision by default?

I have a table computing many numbers with large precision. Because of this, probably, Mathematica consumes a lot of RAM. Is it possible to restrict the precision in any calculations by default (...
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### Why is the N function giving me the wrong result when using WolframScript? [duplicate]

I am using wolframscript.exe to learn mathematica and I would expect the following code to return 0.7071: ...
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### Mathematica accuracy errors when creating data

I created training data for a neural network and below are two errors I got The only code that uses "FindRoot" command is the following ...
• 295
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### General::munfl - Precision lost in LinearModelFit

I am new to mathematica so I am confused regarding the loss of precision in LinearModelFit. In building a linear model with uora (1 or 2) and encodeSeverity (1,2 or 3) ...
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### Solving a determinant to get non-zero roots in a heat transfer problem

I am trying to solve a mathematical model of a heat transfer problem. As an intermediate step there is a characteristic equation in the form of a determinant, which needs to be solved for variable <...
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### How to change Machine Precision digits to meet the tolerances

I am trying to solve for Tcm and Mag by solving nonlinear equations using FindRoot command using following code: ...
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### Problem with the Rank of a matrix after a FindRoot

I am solving a boundary problem defined by a set of four-component vectorial functions. Without going into many details, I have two functions on the left and two on the right of an interface. The ...
101 views

### How to copy and paste numbers with "" mark and use them in calculations, without using N or setting precision every time

Suppose we have run a calculation and get a number like 2.758952615889003 If we then copy-paste this number and do a calculation like ...
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### Different sensitivies from LinearSolve and Eigenvalues. How to conciliate them?

I use the following functions to receive a matrix, and make it symmetric positive definite: ...
95 views

### Understanding Working Precision - two example equations

I am trying to understand how WorkingPrecision works, and in general how very small/large numbers are to be handled. Let me preface I probably do not have ...
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### Conflicting output provided by N[...]

I am trying to evaluate an expression : (-((I (k2 - k1) (-1 + E^(2 I (k2 - k1) \[Pi])))/(-1 + (k2 - k1)^2))) /. {k1 -> 2, k2 -> 7} This gives ...
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352 views

### Dealing with General::munfl errors

Edit: So, while trying to figure out a minimal exmaple, I found out that my main problem was actually unrelated to this and it just happened to be that giant pile of warnings and error messages coming ...
72 views

### How to resolve underflow occurrences?

I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve. ...
• 181
331 views

### Plot a function with very small values, close to zero

I want to plot a function with very small values, close to zero, but even though the limit is -3/2 as x->0, I can't get any ...
• 569
104 views

### Getting max precision limit overflow for a very simple calculation

I've never seen this error on such a simple calculation. Does anybody know how to fix this annoying error?
64 views

### ListLinePlot gives the correct values but N doesn't

I have solved a set of 6 differential equations with DSolve. When I use the table command and produce the results of one of the equations given by DSolve, the ListLinePlot command gives me the correct ...
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44 views

### Unpredictable behavior of numerical error

A comparison of float calculation and exact expression for NumberForm[0.3^2 - (3/10)^2, 18] gives an exact zero for $0.3$. However, ...
• 1,567
90 views

### Unexpected behavior of subtraction with approximate numbers [duplicate]

I'm using the Table command to generate a list of values: FullForm /@ Table[10. - x, {x, 2.7, 2.8, .1}] and I get the ...
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