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25
votes
3answers
2k views

Understanding differences between Maple and Mathematica in examples picked by Maplesoft

I am reading the document "How Maple Compares to Mathematica" found at http://www.maplesoft.com/products/maple/compare/HowMapleComparestoMathematica.pdf. On page 15 there is an example where ...
12
votes
1answer
1k views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
10
votes
2answers
398 views

Floating point operations — division vs multiplication; how do they affect accuracy?

Given two functions: f[x_] := x ((x + 1)^(1/2) - x^(1/2)) g[x_] := x/((x + 1)^(1/2) + x^(1/2)) Which one is more accurate? Side note: If you could explain why, ...
7
votes
1answer
185 views

Law of Cosines to determine angle change along spiral

The Spiral I'm trying to place circles along the outside of an Archimedean spiral. Shown below: ...
6
votes
2answers
147 views

Large Number times Tiny Number

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

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
6
votes
1answer
99 views

Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?

Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
6
votes
0answers
59 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
1answer
449 views
4
votes
1answer
113 views

NExpectation not up to expectations with Boole or Conditioned

Context I am interested in computing numerically the number of extrema at a given threshold for random fields. These numbers are expectations of MultinormalDistributions. Problem This integral ...
3
votes
1answer
333 views

N[number, 100] does not give 100 decimal places [duplicate]

Please look at this computations: a = N[Sqrt[2], 20]; N[a^2, 100] The output is 2.0000000000000000000, which is apparently not $a^2$ to 100 decimal places. ...
3
votes
1answer
294 views

Could the PrecisionGoal for NDSolve be a negative number?

The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
3
votes
3answers
216 views

SetAccuracy behavior

I'm puzzled by the output I get from SetAccuracy. According to the documentation, when SetAccuracy is used to increase the ...
3
votes
1answer
218 views

Strange behaviour of PolyLog Function

I discovered some strange behaviour of the PolyLog[] Function in Mathematica which seems to me like a bug in the function implementation. It looks like ...
3
votes
1answer
41 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
0answers
91 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 ...
1
vote
1answer
84 views

Option: number of digits

The command NestList[Cos, 1.5, 10] produces the list: ...
1
vote
1answer
88 views

Calibrating Precision in calculations

As the title says, I encounter an irritating problem which has to do with the accuracy or the precision used in the calculations. To be more specific, I have the following code: ...
1
vote
1answer
182 views

How can we ensure the result of Mathematica is exactly correct?

This is an example, I plot a function and find it has a defect when x approximates 400. Plot[Cos[.3 x] Exp[-0.01 x], {x, 0, 1000}, PlotRange -> All] Another ...
1
vote
1answer
61 views

User defined functions and decimal places displayed

I have a couple of complicated user-defined functions, one which calls the other, and I wish to control the number of decimal places displayed when I call the "mother" function. I have tried the ...
1
vote
1answer
79 views

How to solve the warning problem and obtain real roots without imaginary part?

I am trying to solve a equation with Newton's method via FindRoot, and the codes are: Define the functions: ...
1
vote
1answer
87 views

How do I craft this constant to a specific accuracy?

An earlier post was migrated to Physics.SE and we determined that if this converged, we would have a constant close to the mass of the proton in kilograms. This constant is constructed by summing the ...
1
vote
1answer
562 views

Increasing number of decimal places in Manipulate input

I've made a Manipulate app. in Mathematica where I vary the value of a function f(a) by varying the parameter a. However, I seem to only be able to edit my input for a for a value up to 5 decimal ...
1
vote
1answer
66 views

Inaccuracy of Piecewise function? [duplicate]

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

How accurate is Collect?

Background: I am trying to compute the Lyapunov exponent for the logistic map given by \begin{equation*} x_{n+1}=F(x_n)=ax_n(1-x_n) \end{equation*} The formula for the Lyapunov exponent for a given ...
1
vote
0answers
137 views

Choosing PrecissionGoal and AccuracyGoal for decomposed integral with NIntegrate

Assume I have a complicated integral $I$ which can feature all kinds of difficulties like infinite interval, rapidly oscillatory integrand, integrable singularities and numerically almost singular ...
0
votes
1answer
35 views

Accuracy and WorkingPrecision

Observe that ...
0
votes
1answer
42 views

How to check the decimal accuracy of result? [duplicate]

I am trying to check if the result is enough accurate to use. I need an accuracy of 10^-6 from some numerical method. Something like root finding algorithm. But how do I check that in mathematica? I ...
0
votes
0answers
49 views

Handling Accuracy and Simplifying

I have the following problem. I have a system of non-linear equations that I log-linearize around a certain point, let's call it point A, using a function that I ...
0
votes
0answers
33 views

the default option of NDSolve

How should I find out what the default value of Accuracy and Precision is in the NDSolve? I have a pde that when I asked it to solve for me the equation with a special Accuracy and precision it gave ...
0
votes
0answers
116 views

Getting increased accuracy for roots of determinant

I have a matrix $a(\kappa)$ from which I am trying to determine $\kappa$ by using the equation $det(a(\kappa)) = 0$. The matrices I deal with are on the order of 100 X 100 to 500 X 500. Originally I ...