The tag has no usage guidance.

learn more… | top users | synonyms

37
votes
3answers
7k views

Understanding differences between Maple and Mathematica in examples picked by Maplesoft

I am reading the document How Maple Compares to Mathematica. On page 15 there is an example where Mathematica produces wrong results. Does anybody know why? MAPLE: MATHEMATICA: Also on page 17 ...
21
votes
1answer
2k views

AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
16
votes
0answers
185 views

Is manual adjustment of AccuracyGoal and PrecisionGoal useless?

This is a problem confusing me for years. AccuracyGoal and PrecisionGoal are two options that I never truly understand and, to ...
13
votes
2answers
613 views

more numerically accurate inverse matrix

I encountered the following matrix mat = {{2, 2.161209223472559` + 1.682941969615793` I}, {2.161209223472559` - 1.682941969615793` I, 2}} and ...
13
votes
1answer
171 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 ...
12
votes
1answer
270 views

How to add AccuracyGoal and PrecisionGoal options in a numerical function?

There are many built-in functions that contain AccuracyGoal, PrecisionGoal and ...
10
votes
2answers
747 views

Why is Mathematica destroying this graph?

Here I have a picture of a function I graphed: reg[x_,y_]:=(x^2+y^2)Cos[4ArcTan[y/x]]; Plot3D[reg[x,y],{x,-2,2},{y,-2,2},AxesLabel->Automatic] And here is ...
10
votes
2answers
935 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, ...
8
votes
1answer
463 views

How trustworthy is NMaximize?

Suppose I solve a constrained optimisation problem using NMaximize. How confident can I be of the accuracy of the result? For concreteness, suppose that F,G are (...
8
votes
1answer
227 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 ...
8
votes
1answer
116 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. ...
8
votes
0answers
139 views

Why has Version 10.3 precision reduced?

In version 7.0.1.0 and versions 10.0 and 10.1 the following is produced: ...
7
votes
2answers
296 views

NIntegrate fails to converge under almost any PrecisionGoal, MinRecursion etc. How can I trust the result?

I have been getting some ideas by reading other related questions in the forum, but the integral I have to do is not converging in many cases. The integrand is of the form: ...
6
votes
2answers
164 views

Large Number times Tiny Number

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

Cannot Get Numerical Results to Match

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

Accuracy of Grad-Shafranov PDE's NDSolveValue over implicit region

Context I need to solve for the toroidal flux of the magnetic field above an accretion disc. For this purpose, I define the region over which the flux is non zero, ...
6
votes
0answers
77 views

Negative accuracy numerics ( 0``-128 notation )

What does it mean to have a negative accuracy number? I understand 0``128 to mean "the number zero to 128 decimal points". Mathematica corroborates this: ...
5
votes
3answers
297 views

SetAccuracy behavior

I'm puzzled by the output I get from SetAccuracy. According to the documentation, when SetAccuracy is used to increase the ...
5
votes
1answer
707 views

How to improve the solution of a double pendulum system

First, the code: ...
4
votes
1answer
121 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 ...
4
votes
1answer
97 views

NDSolve returns asymmetric solution to a symmetric equation

I am trying to find the potential of a conducting cylindrical electrode by solving the Laplace's equation. Both, the boundary conditions and the equation are symmetric w.r.t. the change $r\to-r$. ...
4
votes
2answers
80 views

Is there a way for accuracy backtick notation to accept variable inputs?

Backtick notation uses 1.0``20 to give 1 with 20 places of accuracy after the decimal point. But what I want is ...
4
votes
0answers
85 views

Improve Accuracy of FindRoot

This is a follow up question to an earlier questions I asked. The link is: Product of $N\ 2 \times 2$ matrices and subsequently solving an equation dependent on the product As I am new here, I am not ...
4
votes
0answers
484 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
4
votes
0answers
144 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 ...
3
votes
3answers
336 views

3D Gamma function

I try to plot the following function: Plot3D[Gamma[1+0.5*(n+m)]/Sqrt[Gamma[1+n]*Gamma[1+m]],{n,0,1000},{m,0,1000}] I expect that for m=n and near to it the value ...
3
votes
1answer
530 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. What'...
3
votes
1answer
459 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
1answer
51 views

My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
3
votes
1answer
237 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 ...
3
votes
1answer
348 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
2answers
105 views

Unexpected behavior from Accuracy

This is my code Table[With[{x = 10^n + 1/17}, N[x, {Infinity, 5}]], {n, 0, 5}] // Column Or like this ...
3
votes
1answer
65 views

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

Why is it so, N[Eigenvectors[{{1., 0.5, 4.}, {2., 1., 2.}, {0.25, 0.5, 1.}}]] returns: ...
2
votes
2answers
291 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
3answers
195 views

What's the proper way to 'cut out' an irrelevant part of an integral, so I don't run into problems with precision?

I'm doing a numerical integration that involves an integrand with a few exponentials whose values over the integration region range enormously. I'm really only interested in the part of the range that ...
2
votes
1answer
98 views

Funny behavior when computing dot product of coefficients with high-order polynomials

I have a similar problem to Funny behaviour when plotting a polynomial of high degree and large coefficients. However, the thing being evaluated is not just a polynomial but a dot product of some ...
2
votes
0answers
31 views

Use of AccuracyGoal & MachinePrecision in NIntegrate

I just learned about the Inverse Symbolic Calculator and it seems like a very useful tool. For example, to find an analytic solution to $$ \int_0^{\infty } \frac{1-e^{-x} (x+1)}{\left(e^x-1\right) \...
1
vote
3answers
626 views

Setting the Accuracy of calculations

I need to optimize an expression that involves a number of trigonometric functions and Exp[]. How do I make sure that all my calculations have an accuracy of 120-...
1
vote
1answer
224 views

Precision while calculating Fourier transform

I'm trying to understand how precision works in Mathematica. Particularly I'm calculating discrete Fourier transform using the Fourier function and calculating it "...
1
vote
2answers
73 views

Error In polynomial Root Finding

I have a polynomial in y like so: 2.00855*10^20 + 6.89796*10^20 x y + (5.17347*10^20 + 5.92241*10^20 x^2) y^2 - 1.4806*10^21 x y^3 + 7.77316*10^20 y^4 == 0 I ...
1
vote
1answer
109 views

Option: number of digits

The command NestList[Cos, 1.5, 10] produces the list: ...
1
vote
1answer
95 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
196 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
832 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

Accurate Integration of 2D interpolating function with weighting

I want to integrate a 2D interpolating function received from NDSolve[]. To illustrate my problem I will give a simple example: ...
1
vote
1answer
89 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
92 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
92 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
84 views

Inaccuracy of Piecewise function? [duplicate]

I have the following issue and can't find a solution so far. ...
1
vote
1answer
129 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 ...