# Questions tagged [numerics]

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

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### Find roots of a system equation involving Bessel functions

I'm trying to find the roots (a_n,b_n) of a system involving Bessel functions. I tried to obtain a list of the n-first roots in mathematics with FindRoot, but I only get one root, how can I get the ...
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### First few smallest eigenvalues of a large dense symmetric matrix

I construct a large (say 2000x2000) matrix M whose entries are real random variables drawn from a certain distribution. Most of these values will be nonzero, so <...
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### Solving 2D Coupled Nonlinear SO Coupled Equation

I am trying to solve coupled nonlinear SO coupled equations in 2D from the following two papers https://arxiv.org/pdf/2105.08849.pdf and https://arxiv.org/pdf/2109.00491.pdf. They have given an input ...
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### Constructing NxN tridiagonal block diagonal matrix with N is a variable [closed]

Hi please can someone help me writing a program of generating a tridiagonal block matrix with dimension of NxN where N is a variable can be 50, 100, 200, 300...etc , Well I don't know how I'm a ...
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### How can I solve an equation numerically for a range of x-values and multiple initial root guesses?

The following implicitly defined equation has both real and complex roots: $$\frac{0.5}{(y + x)^2 - 0.3x^2} + \frac{0.5}{(y - x)^2 - 0.3x^2} - \frac{1}{x^2} = 1$$ I am trying to solve it numerically ...
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### Validation of the Laplace inversion and storage in a table or an array

I tried to validate this function from 0 to 50 but it takes very long time, is there a faster way to validate this function for t from 0 to 50 and add them in a list? ...
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### Cholesky with complete pivoting?

I'm looking for an implementation of Cholesky decomposition with complete pivoting. It is the lev3pchol.f function added in Lapack 3.2 (working note) It has an ...
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1 vote
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### Inverse Laplace in mathematica

I can't even get an inverse Laplace for this expression numerically in mathematica, is there a way to inverse this equation below? I have also tried to use fixt talbot package for a numerical ...
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### Orthogonalizing without normalizing part 2

After some searching I couldn't find an existing solution that lets you compute orthogonal (not orthonormal basis) without computing huge performance penalty relative to ...
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### Numerical solution of the inverse contour plot

I have a function $f(u,v)$ on some domain of $(u,v)$ and would like to find (numerically) the set of couples* $(u_0,v_0)$ s.t. $f(u_0,v_0)=0$, for instance (just and example to illustrate, in practice ...
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### Obtaining numerically and efficiently a large number of zeroes

I'm trying to find zeroes numerically, and wrote a small code (see below). The code works reasonably fast for finding a few zeroes (set parameter Msites=20 and find ...
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### Cholesky/LDLt that works for singular matrices?

TLDR When given $A=X'X$ decomposition, user298737 works by relying on QRDecomposition on $X$. If we didn't have this decomposition, one could use QR to get full-rank part of $A$ and use Cholesky on ...
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### How to define a function to be numeric when the input is purely symbolic

My goal is to have NumericQ[h[j]]=True for any j regardless of whether j may be symbolic with no defined value. Setting NumericQ[h[j_]]=True does not work and as I understand the NumericFunction ...
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### Simultaneous nonlinear fitting of two datasets to two trial functions with shared parameters

I'm relatively new to mathematica and stack exchange. Problem Generally my problem concerns finding a simultaneous fit of multiple functions to multiple datasets with shared parameters. I have looked ...
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### Strange issue with NSolve

Please can someone explain to me why the first of the following fails to run (just spitting back the input without warnings/errors), while the second executes successfully? ...
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### How to detect the positive solution to this logistic boundary value problem

I am trying to find the positive solution to this nonlinear ODE. Theoretically, it has been proven that this problem has a unique positive solution for lam large. But, Mathematica can detect only the ...
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### General::munfl: - too small to represent as a normalized machine number error

I've been working on this code and finally got it to a point where it produces something. But there seems to be an underflow problem. I believe this happens when Exp[] is used and tried to fix it to ...
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### Iterative simultaneous numerical optimization of two functions

p = y 10 - 2 x^2 + 5 x; q = 20 y x - y^2 + 2 x; I want to maximize both functions simultaneously (Maximise p to get x and Maximise q to get y). I know that I could ...
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### Using a compiled function in NMinimize

I can get NMinimize to work with compiled functions in simple cases. This works with a constraint: ...
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### Vastly different runtime when evaluating $\mbox{}_3 F_2$

This question is a follow-up to a previous question. I am interested in numerically evaluating the hypergeometric functions: ...
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### Mathematica ignores precision requirement when evaluating a Legendre function

Bug persisting through 13.1.0 [CASE:4953269] When attempting to calculate a certain associated Legendre polynomial within a given precision, Mathematica seems to ignore it if the argument is ...
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### Numerically checking if expression is 0

I ended up with the example below after some debugging. An expression at the end, Norm[A . X1 + X1 . A - B] is zero. However, using ...
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