# Tagged Questions

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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 ...
2k views

### AccuracyGoal, PrecisionGoal, WorkingPrecision and NDSolve

I'm trying to understand exactly what WorkingPrecision, AccuracyGoal and PrecisionGoal mean ...
176 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 ...
587 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 ...
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 ...
269 views

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

There are many built-in functions that contain AccuracyGoal, PrecisionGoal and ...
745 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 ...
925 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, ...
442 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 (...
222 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 ...
115 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. ...
273 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: ...
234 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: ...
164 views

### Large Number times Tiny Number

A (maybe noob) question: Let a = 1234567891234567889998.5 b = 1234567891234567889999.5 Mathematica (v8) yields for ...
334 views

### Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
163 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, ...
131 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: ...
77 views

### Negative accuracy numerics ( 0-128 notation )

What does it mean to have a negative accuracy number? I understand 0128 to mean "the number zero to 128 decimal points". Mathematica corroborates this: ...
292 views

### SetAccuracy behavior

I'm puzzled by the output I get from SetAccuracy. According to the documentation, when SetAccuracy is used to increase the ...
705 views

### How to improve the solution of a double pendulum system

First, the code: ...
120 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 ...
95 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 $r\to-r$. ...
80 views

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

Backtick notation uses 1.020 to give 1 with 20 places of accuracy after the decimal point. But what I want is ...
79 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 ...
438 views

### Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
143 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 ...
333 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 ...
525 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'...
451 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 ...
50 views

### My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
227 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 ...
347 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 ...
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 ...
64 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: ...
77 views

### In NMinimize, how can I efficiently handle NIntegrate errors for non-integrable functions?

I am using NMinimize to find parameters that minimise the integral of a function in the least squares sense: ...
286 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 ...
193 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 ...
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 ...
29 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) \...
619 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-...
220 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 "...
70 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 ...
108 views

### Option: number of digits

The command NestList[Cos, 1.5, 10] produces the list: ...
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: ...
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 ...
830 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 ...
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: ...
88 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 ...