# Tagged Questions

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

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### Is MatrixExp[m,v] always faster than MatrixExp[m].v?

For non sparse matrix m, is MatrixExp[m,v] supposed to be faster than MatrixExp[m].v? This seems to be true only if m is purely real or imaginary. ...
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### Multiplication non-deterministic?

I have two vectors of 134 elements each ($mu$, and $gt$). $mu$ contains Integers, and $gt$ contains machine precision Reals. I execute the following simple expression multiple times without changing ...
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### Numerically parameterize portion of $F[x,y]==0$ [duplicate]

I have a relatively complicated function of two variables F[x,y] whose zero locus contains a number of intersecting paths in the $x,y$-plane. A problem I've been ...
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### Copy-pasting a floating point number [duplicate]

Here is a behavior of the Mathematica front end which confuses me. Type N[Sqrt[2]] The displayed output is 1.41421 ...
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### How to implement custom integration rules for use by NIntegrate?

How can NIntegrate be extended with custom implementation of integration rules? This answer of the question "Monte Carlo integration with random numbers generated ...
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### Understanding difference between NIntegrate result and home-cooked Simpson's rule

In this question I am asking about the different results I get between NIntegrate-ing a function of two variables vs. "doing it myself" with my own implementation ...
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### 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 ...
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### Numerical fitting trajectory to model that has NDSolve

I have a model which describes the motion of an object on a plane. ...
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### How to calculate this complex expression?

I have a complex expression as follows, ...
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### Determining the value at which a function becomes non-real or undefined

If I have a function $f(x)$ that I only know numerically and that returns a real value for some range of values $-\infty < x \leq a$ and complex values for $a < x < \infty$, how can I ...
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### Using loops to draw multiple polygons and discretizing them

I am trying to plot the first eigenvalue of the Laplacian operator with zero Dirichlet condition on following figure against decreasing values of $\varepsilon$. I used ...
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### Wrong numerical results from LegendreP

{Cos[Pi/180] // N, LegendreP[46, 0.9998476951563913`], LegendreP[46, Cos[Pi/180]] // N} give ...
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### Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions

Bug introduced in 7.0 or earlier and persisting through 10.4.1 This is a follow-up to this question regarding numerical instabilities occurring with modified Bessel functions. In trying to explore J....