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44
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: ...
13
votes
2answers
331 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. ...
8
votes
2answers
193 views

Error computing sum of sum of digits

I've defined a function that computes the sum of the base-b digits of n: DigitSum[n_, b_] := Total[IntegerDigits[n, b]] Then I defined a function that computes ...
8
votes
1answer
285 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
241 views
6
votes
3answers
1k 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
232 views

A problem about fixed point iteration theory

Description Recently, I have been learning a couse called "Numerical Analysis". The fixed point iteration theory was introducted to solve the ...
6
votes
2answers
148 views

Large Number times Tiny Number

A (maybe noob) question: Let a = 1234567891234567889998.5 b = 1234567891234567889999.5 Mathematica (v8) yields for ...
6
votes
1answer
100 views

Numerical Integration different in Mathematica version 9 and 10 with same options

I have noted that the same function with the same settings gives me different results in Mathematica version 9 and 10. This involves integrating numerically interpolating functions and so on. Here a ...
6
votes
2answers
283 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
6
votes
0answers
61 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
1k 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
489 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: ...
5
votes
1answer
136 views

Numerical error in Mathieu functions

Consider the MathieuCharacteristicA function, which is a piecewise function according to the documentation. The discontinuity happens at integer number. ...
5
votes
1answer
59 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
6answers
1k views

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

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. ...
4
votes
2answers
186 views

Why does N[Re@f] give complex result?

Consider this code: ...
4
votes
3answers
209 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
93 views

Is the divergence between Round and setting an explicit precision intentional or a bug?

Introductory remark: I take it (from Mathematica's online documentation), that Precision is effectively the number of significant digits, as seen by the system. ...
4
votes
1answer
100 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
160 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
2answers
61 views

numerical precision in output file

I want to write the numerical results of a computation to a file which is to be read in Fortran. The data looks like: ...
4
votes
1answer
199 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 ...
4
votes
1answer
277 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 ...
4
votes
1answer
881 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. ...
4
votes
3answers
175 views

Importing High Precision (22 digits) data from a file

I want to import list from a file and I am using ReadList but my data is in format like this 8.2457409790900004e+08 but it i being imported like $8.24574*10^8$. Is ...
4
votes
0answers
37 views

Change system options in package

I use Mathematica mostly for numerical calculations, and sometimes the performance of numerical calculations can be greatly improved if the high-precision arithmetic can be switched off by ...
4
votes
0answers
50 views

The change of precision doesn't work in ParallelDo. Is it a bug in Parallel?

Cross-post: http://zhidao.baidu.com/question/2075301703219376588.html Input: ...
4
votes
0answers
98 views

Precision problem while evaluating RegionMember or Element in V10

I'll try to give you a background on where the problem occured. The problem itself is defined near the end of the post. I'm running a sort of a simulation of a particle in a box. I finally got my ...
3
votes
4answers
187 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
2answers
125 views

Explicit digit-count (precision) of real number

I'm trying to do something which seems like it should be simpler than it is (at least in my attempts at it). I have some code where I read in a list of numbers generated for me by a coworker. These ...
3
votes
2answers
883 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 ...
3
votes
1answer
55 views

Is it possible to change the MinPrecision in command “Compile”?

I'm using "Compile" to do some numerical calculation and I need high Precision. I was wondering if it is possible to change the Precision in command "Compile" to some $MinPrecision?
3
votes
1answer
230 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
2answers
141 views

Increase precision for a entire notebook

I am quite a newbie and it is taking me so much time to understand what I need to do to achieve something really simple and I still haven't found it. I run a dynamic model of a metabolic pathway in ...
3
votes
1answer
42 views

Deferent results depending on the input form of the matrix [closed]

Why is it so, N[Eigenvectors[{{1., 0.5, 4.}, {2., 1., 2.}, {0.25, 0.5, 1.}}]] returns: ...
3
votes
1answer
38 views

Is it possible to generate a message when precision upgrade occur?

I use Mathematica mostly for numerical simulation, so most of the time double precision (or machine precision) is enough for me. Mathematica has this nice feature of automatically upgrade to arbitrary ...
3
votes
0answers
47 views

WorkingPrecision in LogLogPlot creates wrong plots

I seem to have found a bug with LogLogPlot in version 10. If I specify a working precision, the function produces total garbage. Here is a simple example. The first case, without WorkingPrecision ...
3
votes
0answers
94 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
4answers
141 views

Precision problem with numerical solution of a differential equation

I want solve $$ 2\sqrt{|\gamma|}x = \int_{1}^{t} dy \sqrt{\frac{1+2|\gamma_2|y}{y^2(1-y)}} $$ where $0<t\leq $1. I'm using a for cycle to evaluate t, calculate the integral and the assign the $x$. ...
2
votes
2answers
111 views

How to get the digits after the decimal point

I have N[Sqrt[2], 8] which outputs 0.4142136 How do I get the 4142136 part out of it? I ...
2
votes
2answers
141 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
124 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
1answer
57 views

Working precision and pure functions in FindMinimum

I have this function: fun = (# - 5.0)^2.0 & Then, I want to find the minimum: ...
2
votes
1answer
59 views

Range and decimal digits [duplicate]

When I set Plot[Sin[x], {x, -2, -1}, Frame -> True, Axes -> False, FrameTicks -> {{Automatic, Automatic}, {Range[-2, -1, 0.2], Automatic}}] I ...
2
votes
1answer
56 views

Precision of NIntegrate

At the moment I am considering a 'difficult', highly-oscillatory integral in Mathematica. It calculates the integral without any complaints. However, I am also trying out a numerical method with which ...
2
votes
1answer
35 views

FindMinimum's WorkingPrecision behaviour

I discovered the following behaviour when using FindMinimum for constrained optimization: ...
2
votes
0answers
36 views

Precision loss in FourierDCT

I have high precision data that I want to do Fourier transform with, but it looks like the precision is lost dramatically. ...
2
votes
0answers
125 views

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

I want to calculate with simple double floating point precision. ...
1
vote
1answer
87 views

Option: number of digits

The command NestList[Cos, 1.5, 10] produces the list: ...