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42
votes
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: ...
12
votes
2answers
252 views

Why do NumberForm and Round apparently use different tie-breaking methods?

When rounding numbers (for example, rounding a real number to the nearest integer), the "round to nearest" rule is usually used. For example, 1.4 is rounded down to 1 and 1.6 is rounded up to 2. ...
7
votes
1answer
234 views

Confused by (apparent) inconsistent precision

$$ e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925 $$ E^(Pi Sqrt[163.0]) N[E^(Pi Sqrt[163.0]), 35] NumberForm[E^(Pi Sqrt[163.]), 35] returns ...
6
votes
3answers
172 views
6
votes
3answers
954 views

Strategies to solve an oscillatory integrand only known numerically

I have an integrand that looks like this: the details of computation are complicated but I only know the integrand numerically (I use NDSolve to solve second ...
6
votes
2answers
145 views

Large Number times Tiny Number

A (maybe noob) question: Let a = 1234567891234567889998.5 b = 1234567891234567889999.5 Mathematica (v8) yields for ...
6
votes
2answers
248 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
6
votes
0answers
56 views

Is there a way to get BSplineFunction beyond MachinePrecision?

I have been using BSplineFunction (Mathematica 8) to generate a smooth representation of some data, which I might then do some further processing on. As I ...
5
votes
2answers
616 views

How to convert a string of number into real numbers without precision loss

I searched and did not find similar answers which can resolve the 'no precision loss' issue. A sample string is: ...
5
votes
1answer
55 views

Mysterious behavior of Precision for complex arrays

Mysterious behavior of Precision: {{1.0+I*0.0},{0.0+I*0.0}} // SetPrecision[#,30]& // Precision // Print; ...
4
votes
3answers
153 views

Increasing the precision of a calculation

Clearly I have misunderstood how to do this: I seem unable to understand how to get more digits out of a calculation and I can't see why - the following piece of code illustrates the issue. ...
4
votes
1answer
84 views

Issues with $MachineEpsilon

I'm attempting to add $MachineEpsilon to numbers I am pulling from the domains of 3 interpolating functions. I pulled 3 numbers, and for one of these numbers adding ...
4
votes
1answer
139 views

Padding plot ticks with zeros on the right

I would like to know how can I make a real-valued plot tick pad with a zero to the right of the decimal point on integer values. This is what I have: ...
4
votes
1answer
178 views

How to find derivative of a numerical solution, where precision is ambiguous?

I am trying to take the derivative of a numerical solution. I am concerned that the way I'm doing this may be problematic due to numerical error; I think there must be a better way but I'm not very ...
3
votes
5answers
959 views

Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do? [closed]

The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration. ...
3
votes
4answers
139 views

AccountingForm w/o significant figures

Basically I want to build a chart like something I would do in Excel. It should look like this: Here is the formula I'm using and what I've done so far ...
3
votes
1answer
189 views

Numerical Error with Large Matrices

I am writing a Finite Element Analysis program in Mathematica. The code involves handling a large matrix with large entries. I get an error when I try to use Mathematica's "LinearSolve" to solve a ...
3
votes
1answer
237 views

ParallelTable and Precision

I'm using ParallelTable[] to calculate a function over a range of my parameters , ($\omega,\ell$). This seems to be working well (in terms of speed increase) except ...
3
votes
1answer
386 views

How to set the working precision globally? $MinPrecision does not work

I want to increase the precision globally to 50 at least, but $MinPrecision does not work. ...
3
votes
1answer
349 views

ReadList can't read from file containing high-precision Reals

I want to read a file which contains seven columns of real numbers. Mathematica seems to have a problem with the high precision I need. My code: ...
3
votes
0answers
84 views

Tools for Stability/Automatic Error Analysis in Mathematica

I have a longer analytic expression in several variables containing special functions and others. Does Mathematica bring tools - or are there any packages - to examine the stability when I evaluate ...
2
votes
2answers
103 views

NIntegrate - WorkingPrecision

I am trying to NIntegrate this expression. It is very close to zero, and so gives all possible types of errors. More precisely, ...
2
votes
1answer
102 views

Why the EuclideanDistance of these 2 exact points generates the warning N::meprec?

The two points are: pts = {{1/4 (-1 - Sqrt[5]), Sqrt[5/8 - Sqrt[5]/8]}, {1/4 (-1 - Sqrt[5]), -Sqrt[5/8 - Sqrt[5]/8]}}; EuclideanDistance @@ pts ...
2
votes
2answers
737 views

Problem with setting working precision in NIntegrate

I want to obtain a good numerical approximation (up to 10 decimal place would be ok for me) to an integral: $$ \int^{\infty}_{0} f(r)r^2dr $$ I am using the function $f(r)$, which is related to the ...
2
votes
0answers
102 views

how to calculate with just double floating point precision [duplicate]

I want to calculate with simple double floating point precision. ...
1
vote
2answers
67 views

SetPrecision — different values subtracted from unity gives same value

How are my results possible? CODE: SetPrecision[FibersFailedNew, 40] 3.612171938234261799295174910010284760488*10^-16 ...
1
vote
1answer
87 views
1
vote
1answer
115 views

ListPlot with high precision

I have a list of numbers, e.g. {{1.,0``27.698970004336022},{2.,0``27.698970004336015}} but usually much longer, suitable for ...
1
vote
1answer
141 views

Numerical Instability?

Current Status Please skip ahead to Update 2: the key questions are now: 1/ Why does Mma generally fail to find the minimum for a well behaved function when the function does not have infinite ...
1
vote
1answer
147 views

Output precision

I've solved some equations using FindRoot and then computed some values. Now when I print the output, I only get a certain precision {{0.01, 496.983, 61.3147, ...
1
vote
1answer
55 views

Inaccuracy of Piecewise function? [duplicate]

I have the following issue and can't find a solution so far. ...
1
vote
1answer
43 views

ReadList error with negative very small numbers

When I try to import data with ReadList from a file containing very small numbers (~10^-318), positive data is handled well, ...
1
vote
1answer
220 views

Export image data precision

I'm sure there is a very easy way to control this, but I have been searching for an hour now without luck. I plot a function and export it to get a table that I can use in TikZ. ...
1
vote
0answers
32 views

Frontend displays wrong number digits [duplicate]

How do I change the default precision in Mathematica? Somehow the setting has been changed to 1 digit, so if I type Timing[...] I get {1., ...} which is ...
1
vote
1answer
134 views

Plot periodic function from Dirac delta function [duplicate]

Sorry for my bad english. I need to plot periodic function from dirac delta: δT(t)=∑δ(t–n*T), where T - is a constant, and n=-20..20 And after them, plot new function fd=f(t)*δT(t) - discrete signal ...
1
vote
1answer
113 views

Working precision for each variable

How can I define working precision for each variable individually for example: Maximize[x y< 100, {x, y}] where the working precisions for ...
0
votes
2answers
261 views

Problem with working precision

I have tried to resolve the problem of the following link How can I solve precision problem I can tell the problem described in that link shortly here, It's no mater how many precision is there after ...
0
votes
1answer
97 views

How can I obtain more significant digits? [closed]

I type f1[x_] := 12 x^5 - 975 x^4 + 28000 x^3 - 345000 x^2 + 1800000 x N[f1[15.5], 15] and obtain 3.74112*10^6 BUT It´s not true!!! the result is larger than ...
0
votes
1answer
113 views

How to get more accurate orthonormal eigenvectors?

I have a matrix M with real entries in MachinePrecision. I compute its eigenvectors and construct matrix ...
0
votes
0answers
43 views

Precision of sliders in WebMathemtica

I have been developing a manipulate plot to put on the web. One of my parameters varies over a small interval, {{D32, 2.38*10^-3, "D32"}, 0.001227, 0.0049108}. This ...
0
votes
1answer
44 views

How to make a discretized NMinimize more precise

I am using Mathematica for physics research and I want to minimize a Hamiltonian equation with respect to two variables (I have also discretized the problem). I have a single constraint. When I plot ...
0
votes
0answers
52 views

Meaning of backtick in conjunction with units [duplicate]

In this fragment from an equation solution the backtick is used twice: ...
0
votes
0answers
21 views

Ignore $MinPrecision when using Print

I have a function that contains a For loop and sometimes takes several hours to run. It's important that I keep a high precision, and I insert ...
0
votes
0answers
28 views

How to get precision for a small calculation? [duplicate]

For pc1 and pc2 this gives the answer to only four decimal places. How can I get better precision? ...
0
votes
1answer
83 views

Truncate a fractional value to particular number of bits?

If I have a fractional value, how can I truncate (not round) that to a certain number of bits, like 8? For example, for Pi 3.141569265359... the fractional part is 0.141569265359... ...
0
votes
0answers
28 views

What is the precision of this number? [duplicate]

In a matrix evaluation, I got the following number. 2.8330574963868513` I understand that the number after ` shows the precision of the output number. But this ...