Questions tagged [precision-and-accuracy]
The precision-and-accuracy tag has no usage guidance.
-3
votes
0answers
50 views
How to design and deal with repeating decimals? [on hold]
Repeating decimals could be represented by fractions.
Given
$
\huge{\frac{1}{3}=0.33333\overset{!}{3}}\tag{1}
$
if multiply $3$ on both sides,is this step wrong?...
6
votes
7answers
934 views
How to display very small numbers in Mathematica?
I am trying to evaluate the function:
$$f(x) = \cos(x) - \mathrm{e}^{-2.7 x}$$
at $x = 1.7 \times 10^{-25}$
and Mathematica keeps returning '0.'
How do I evaluate the expression in a better way?
0
votes
0answers
24 views
A function to create a Symmetric Positive Definite Matrix, from any matrix. Why doesn't it work? [on hold]
I've created the following function with the purpose such that, given any square matrix, it should return the closest(system precision dependent) symmetric positive definite matrix.
...
3
votes
1answer
83 views
Problem with the Inverse CDF of Non-central F Ratio Distribution
In[3]:= n = 5; n1 = 4; n2 = 6; γ = 0.05; α = 1/370;
InverseCDF[NoncentralFRatioDistribution[1, n1 - 1, n1/γ^2],
1 - α - (n - n1)/n2]
During evaluation of In[3]...
4
votes
1answer
77 views
Catastrophic loss of accuracy in Orthogonalize
Context
In connection to this question
I am interested in orthogonalizing known matrices.
As a test case, let us consider the definite positive 15 x 15 matrix mat
...
0
votes
1answer
51 views
Good practice about numerical precision
In one of my calculations, I get -1.11022*10^-16 as one of my eigenvalues for a matrix. It's essentially zero and I suppose I could use SetPrecision to make it zero but I wonder what's a good practice ...
0
votes
1answer
53 views
Increasing MaxExtraPrecision arbitrarily changes numerical result
I am trying to confirm that a function $f$ satisfies a particular differential equation of the type $D f=0$, for some differential operator $D$. I set $Df$ as Diffeq...
0
votes
0answers
30 views
Return the precision of the first non zero digit in a number for measurement error representation function
I'd like to return the precision of the first non zero digit in a number. The motivation is so that I can quickly construct my error notation which is the bracketed notation, e.g.
$x = 1.234$ with ...
1
vote
2answers
124 views
How to avoid this type of change of digits in computed numbers?
Is there a way to avoid the digits being changed?
...
0
votes
1answer
35 views
Inaccuracy in Plot3D
This problem might be well-known - in this case, I would appreciate a link, because I could not find anything. My problem: A certain function (super long and nasty expression) needs to be plotted. ...
5
votes
1answer
81 views
Loss of accuracy in orthogonalisation of polynomials using Orthogonalize
Context
As a mean to understand the growth of structure in the universe,
I am interested in characterising the curvature of random fields such as this one:
For this purpose I start with a PDF of the ...
0
votes
0answers
37 views
0
votes
0answers
26 views
DensityPlot, ScalingFunctions, and small values
Edit: I figured out I can use Rescale to retrieve the plot as well as get the correct plot legend. I still can't figure out how to rescale the axes from 10^-9 to 1 ...
1
vote
2answers
42 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
...
1
vote
1answer
40 views
0
votes
1answer
48 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]]:
...
0
votes
0answers
21 views
Speed and precision with Inverse Laplace transform
I have a problem with an inverse Laplace transform that to me looks like a precision problem when computing with large/small numbers. Scientific background: I would like to compute how photons from a ...
1
vote
1answer
41 views
Performing a FindRoot from Numerical integration
I am trying to evaluate:
FindRoot[Xfnew[γ, w, Hi, mx]*92*10^23*γ^(4/(1 + w)) == 1198/10000, {Hi, hs},
MaxIterations -> 10000]
for some starting value hs,...
0
votes
3answers
28 views
Low precision from function returning matrix
Got a function depending on single parameter "t" defined below which
returns a 2 by 2 matrix
...
0
votes
2answers
61 views
How to deal with the loss of significant digits in this expression with Fresnel integrals?
I needed to solve this integral:
$$\int_1^\infty \frac{dx}{\sqrt{x}} \cos \left(a x-\frac{\pi}{4} \right) \cos \left(b x-\frac{\pi}{4} \right) \cos \left(c x-\frac{\pi}{4} \right)$$
Coming from ...
2
votes
2answers
80 views
What's the smallest positive real allowed in mathematica?
This question may be a bit strange, but in this question, one of the answers suggests substituting some negatives values in a matrix by the smallest positive real number allowed. So, I was wondering ...
0
votes
1answer
40 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....
2
votes
1answer
59 views
Inaccurate zero eigenvalues for 7*7 matrix [closed]
I have symbolic entries for all the elements of a 7*7 matrix. At the symbolic level Eigenvalues gives two zeroes and five others that are extremely complicated. At ...
3
votes
1answer
45 views
Numerical precision problem
I have this simple code:
ep = 1 - 80000000000 (-(199999/200000) + 1/E^(1/200000))
ep // N
-8.27404*10^-8
...
0
votes
0answers
37 views
Solving a system of linear equations in Mathematica regarding the errors of different methods
I have a system of equations, i.e.
0.62243x + 0.51824y = 0.70524
0.71497x + 0.59496y = 0.80996
I have 3 ways to solve this system (there are more but I am ...
0
votes
1answer
75 views
Problem with solving differential equation using NDSolve
I am trying to solve differential equations subject to condition z[0] == 0 and z[tmax] == 10 Pi.
...
0
votes
1answer
41 views
Formatting a list of values and dependent formatting of corresponding errors list
I am making a table of data that I wish to output using TeXForm.
Rather than manipulate the values in LaTeX (e.g. using the ...
3
votes
1answer
53 views
0
votes
2answers
63 views
equal expressions give different numerical result
I have two expressions, and they are really equal:
...
2
votes
1answer
136 views
NIntegrate fails to converge
I am trying to compute this integral for different a with 0.0001<a<0.5,
...
7
votes
1answer
226 views
How does Mathematica determine when to use scientific notation?
I have code that takes an initial guess for a set of parameters to use in a function that I want to minimize, calculates the function, prints the value, recalculates new parameters via the gradient ...
7
votes
3answers
117 views
How to create an Interval object with specific end points?
When creating an Interval object, the end points are automatically widened when an end point is an inexact number. For instance:
...
14
votes
4answers
280 views
Terrible accuracy of DawsonF
DawsonF[30.] returns 0. The correct value is 0.016676...
At least it prints a warning message,
...
1
vote
2answers
38 views
Diagnosing the numerical stability of a function
I have programmed a function f[x] that seems to be very unstable numerically. More precisely, I noticed that for certain arguments in arbitrary precision, the ...
3
votes
0answers
61 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, ...
5
votes
2answers
119 views
Integrating a bivariate distribution over a region bounded by a straight line
Summary of problem: I'm using Mathematica version 8 to try to integrate the bivariate distribution over a region bounded by a straight line. The two random variables are uncorrelated. When I use ...
5
votes
1answer
63 views
DiscretePlot Giving Incorrect Answer
I know similar questions have been asked before about bugs in Integrate, but I'm not sure what the particular problem is here (and whether or not there is indeed a bug). When I perform the integral:
...
5
votes
2answers
330 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 <...
5
votes
2answers
91 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:
...
0
votes
1answer
47 views
0
votes
0answers
59 views
FullForm[1. - (0.3 + 0.4)] gives 0.30000000000000004` [duplicate]
I had a serious error propagation in my computations (Mathematica 10.4.1 Windows 64 bit). After some investigation, I realized the problem comes from something like this: FullForm[1. - (0.3 + 0.4)] ...
1
vote
2answers
66 views
Rounding numbers to certain numbers of significant figures
I have code which outputs numbers, for example,(0.2945847, 0.8647834, 1.6*10^-6) and similar. I would like to take these numbers and round them to 4 significant figures, but I can't find a way to do ...
0
votes
0answers
29 views
Identical expressions subtracted from each other giving small but significant errors
In my current code, I have formed a list of numbers with two different methods. For the first method, I wrote
...
2
votes
3answers
241 views
How can I remove the FindRoot error from my calculations?
If you run my calculations given below
...
0
votes
3answers
92 views
Precision for function
I have a notebook where I have to work with high precision (say, 100). I have tried several methods to define it for the entire notebook, including
...
0
votes
2answers
72 views
Computing a sum with high precision
I am aware that a similar question has been asked, for example, here and here, but none of the proposed solutions solves my problem, so please wait before you mark this question as a duplicate.
...
