# Tagged Questions

Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

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### Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
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### 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 ...
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### Finding the square root of a squared number?

Taking the square root of the square of a number Variable set to a real value I'm wondering why these examples a = -4.3; Sqrt@a² Sqrt@(a^2) Sqrt[a^2] Sqrt[a²] ...
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### Round vs. Floor vs. Ceiling for non-integers non-orders-of-magnitude

I understand that Round give the nearest even integer for cases where the number is between two integers, i.e. Round[2.5] = 2 ...
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### Numerically integrating a list-valued function [duplicate]

I want to NIntegrate a List valued function foo[x] which is only defined for numerical ...
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### Any ideas on how GeneralMiniMaxApproximation is implemented?

GeneralMiniMaxApproximation is used to construct minimax approximations of parametrically defined functions. I am curious about how ...
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### How to speed up Min of DateObjects?

I'm in version 10.0.1 using a Dataset to do some plots and things. For one of the plots I need to get the minimum date of a some filtered set of the ...
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### Infinite base two number to base ten

Suppose I have a base two number that repeats itself every five places (a number $x$ such that $0\le x<1$. For example: $$x=0.101011010110101101011010110101101011010110101...$$ What would be a ...
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### Gamma function computation efficiency?

I wonder what kind of algorithm is used to compute the values for the gamma function. Specifically, I am interested in how the computational load increases when the complexity of the input grows. So, ...
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### Mathematica NDSolve and 'Compile'?

Since the consensus is usually that NDSolve speeds fares badly against compiled code such as c++ ODE solvers using GSL say, is it possible to make up for this lag ...
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### How do I numerically evaluate and plot the Fabius function?

The Fabius function is a well-known example in analysis of a non-analytic function that is infinitely differentiable. I want to be able to numerically evaluate the function for any real argument, as ...
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### Is there no documentation for Method in Eigensystem?

There does not appear to be any documentation on how to use Method in Eigensystem, or at least not in Version 9.0.1 of ...
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### Why doesn't Rationalize work for 0. in Interval?

Same motivation as this q. Why doesn't Rationalize work for 0.? Interval[{0., 1.}] // Map[Rationalize, #, {2}] & ...
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### Numerical error in Mathieu functions

Consider the MathieuCharacteristicA function, which is a piecewise function according to the documentation. The discontinuity happens at integer number. ...
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### Iteration process involving several functions

I would like to carry out a following iteration process: Apply function f1[a_,b_,c_,d_] to a starting list l1={a1,b1,c1,d1}, ...
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### Numerical problems with calculation of function

I have a problem with a calculation which I try to do with Mathematica (8.0.1). I have the following function which describes a cone (with half opening angle theta)...
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### Trouble with shooting method for a 4th-order differential equation

I'm trying to solve the following forth-order ODE with the shooting method: \frac{1}{5}(y-2xy^\prime)=\frac{1}{x}\left\{\frac{xy^\prime}{y}+xy^3 \left[\frac{(xy^\prime)^\prime}{x} \right]^\prime \...
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### Mutual Information involving two matrix states

I basically retrieved the following technique of evaluating the mutual information involving two matrices from this site at http://bmia.bmt.tue.nl/People/BRomeny/Courses/8C080/default.htm The ...
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### 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: ...
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### Display a number in Mathematica 9 in periodic form

I want to display a rational number in Mathematica in periodic style. PeriodicForm isn't working anymore. It worked in Mathematica 5 and now I'm using Mathematica 9....
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### Numerical differentiation methods

Is it possible to write code in Mathematica that implements various differentiation methods (like forward, central, extrapolated, etc.)?
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### Numerical Differentiation using 1500 data points

I have a set of 1500 data points (which are some energy eigenvalues) corresponding to a parameter H0 (which represents magnetic field. H0 values are equispaced going from $-3.0$ to $3.0$ in steps of \$...
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### Strange phenomenon occurring in analytic integration result involving Bessel functions

For the following integral, Integrate[x^2 Exp[-a x^2 - b x^4], {x, -∞, ∞}, Assumptions -> {a > 0, b > 0}] Mathematica gives the following analytic ...
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### Differentiate a numerically defined function

My function is f[a_, b_] := NIntegrate[Sqrt[(Cos[t] - a)^2 + b^2], {t, 0, Pi}] I want to calculate g[1,1] where ...
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### How to cancel floating point factors?

I am currently having problems with some floating points. I have a function, which gives as an intermediate result (for example) ...