Questions tagged [inverse]

Questions on exact, symmetric reversal of a definition or functional mapping (i.e. the original form is returned when applied twice). Use this tag for issues on inversion of Mathematica expressions, or general inversion of math constructs.

29 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
8
votes
0answers
1k views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
5
votes
0answers
459 views

Inverse of piecewise function with pieces invertible on specific domain

I have piecewise continuous function defined below: f=Piecewise[{ {15 + 1/6*(# - 3), # <= 27}, {# - 12 + 4 * Exp[-5/24*(#-27)], 27 < #} }]; This ...
5
votes
0answers
640 views

How to invert a matrix with 100 trillion elements?

I have a $10^{7}\times 10^{7}$ matrix with the following properties: it is sparse it is gamma-5 it is almost Hermitian. If $M$ is the matrix we are trying to invert, we know $M=A M^{\dagger} A$ ...
2
votes
0answers
55 views

InverseRadon function - possible bug?

I have to calculate a 2-dimensional radially symmetric distribution from a single projection. I know that InverseRadon should actually do the job, but I get the ...
2
votes
0answers
37 views

establish matrix and inversion of a uppertriangularized matrix

Trying to create an uppertriangularized matrix with Poisson Distribution, find its inverse and multiply the inverse by a vector, i.e. ...
2
votes
0answers
412 views

Approximate inverse of large sparse matrix with small diagonal element

I need to find inverse of a large sparse matrix with small diagonal element. I follow this question - Is there any way to obtain an approximate inverse for very large sparse matrices? and try to use ...
2
votes
0answers
387 views

Invert a transcendental function

I have tried Reduce and Solve in Mathematica, as well as have a long list of tries in Maple, but cannot seem to get anywhere ...
1
vote
0answers
71 views

Integration that involves inverse of a big symbolic matrix

I have a $300\times300$ symbolic matrix and I want to calculate its inverse matrix. It has been two days and Mathematica is still executing Inverse[T]. $T$ is the name of that matrix. Why am I ...
1
vote
0answers
38 views

Inverting a series

How do I invert the following, \[Rho]=r + b0 Sum[Pochhammer[1/2, k]/(k! ((1 - q) k - 1)), {k, 0, \[Infinity]}] + b0^(1 - q)/(2 q) r^q + O[r^(2 q - 1)] to get $r(...
1
vote
0answers
49 views

Inverse of Normal Distribution CDF incorrect for large value?

I have a function F which is the CDF of the standard normal distribution. The inverse of F should be infinity at 1. However, I ...
1
vote
0answers
93 views

Fast method for getting the inverse function of the Hypergeometric function in Mathematica

I didn't manage to obtain the inverse function for this frightening function: ...
1
vote
0answers
395 views

Inverse of a sparse 21x21 symbolic matrix

I am trying to compute the inverse of the following symmetric sparse(density 0.37) 21x21 matrix involving symbolic expressions in the entries(the variables ...
1
vote
0answers
191 views

How to invert an Elliptic function where the elliptic nome is a function of an independent variable?

I have a Jacobian elliptic function as a function of two independent variables $x$ and $y$. The elliptic parameter $m=m(y)$, $0 \leq m \leq 1$, is also a function of the variable $y$, and thus the ...
1
vote
0answers
402 views

Speeding up inversion of symbolic matrices by invoking caching

Is it possible to reduce the computation time taken to find inverse of symbolic matrices USING CACHING TECHNIQUES accessible (if any)? I am trying to compute inverse of symbolic matrices of size ...
1
vote
0answers
602 views

Automatic inverse for Lambert’s Azimuthal Equal-Area Projection

I’m interested in finding closed-form inverses for map projection equations in general (of course, this is not always possible). I’m hoping Mathematica can help me with some of the trickier ones. As ...
0
votes
0answers
32 views

How to find the Inverse of numeric Function that was created from NDSolve

I'm a newbie to Mathematica and i do have a simple question. I have a function H that was created numerically as solution form NDSolve (like H(R)), and i'm trying to create the Inverse function R(H) ...
0
votes
1answer
50 views

Finding the inverse of possibly non-invertible interpolation function

Consider the following sample code pts = Table[{i, i^2}, {i, -10, 10}]; foo = Interpolation[pts]; Plot[InverseFunction[foo][y], {y, 0, 10}] From the plot, we see ...
0
votes
0answers
20 views

Plotting CDFs of transformed normal random variables

I'm using the following transformed random variables ...
0
votes
0answers
59 views

Inverse::luc Badly conditioned matrix may contain significant numerical errors. Why?

I want to find the inverse of the following matrix, which is given in terms of the following constants: ...
0
votes
0answers
44 views

Solving a System and taking inverse Laplace/Fourier Transforms

I have a set of linear equations for 4 quantities which have been both Fourier transformed and Laplace transformed. The system needs to be solved for the quantities and then each of the quantities ...
0
votes
0answers
23 views

InverseFunction cannot evaluate negative arguments

I have difficulty figuring out where my code fails. I want to obtain $\textbf{ry}$ which is the inverse function of rho (see below). When I input positive values for its argument, there's no problem. ...
0
votes
0answers
38 views

Why does the numerical inverse laplace function FT for small times give erroeous results and what is the alternative

I am trying to do the numerical laplace inverse of a very complicated transfer function, subject to a trapezoidal pulse input. For the sake of understanding, I will use a simple transfer function to ...
0
votes
0answers
56 views

Find inverse of a complicated function

I am looking for an analytic inverse function for ...
0
votes
0answers
115 views

Fourier Transform and Inverse Fourier Transform of Lists

I am trying to compute the Fourier transform of a list, say an array of the form {{t1, y[t1]},.....{tn, y[tn]}}; apply some filters in the spectral components, and then back transform in time domain. ...
0
votes
0answers
73 views

Inverse of Poly Log function? Asymptotic behavior of Poly Log function?

I am unable to answer important questions such as what is the inverse of PolyLog[3/2,z]? I mean can you express the solution to w = PolyLog[3/2,z] (solve for z in terms of w) in terms of functions ...
0
votes
0answers
35 views

Inverting a matrix when its elements are given by difficult expressions?

I have a matrix which is composed by these elements: $$\mathcal{K}_{11} = \frac{3\alpha^{4/3}(4\mathcal{V} - \xi +6\alpha \sum_{k = 2}^n\lambda_k \tau_k^{3/2})}{4(2\mathcal{V}+\xi)^2(\mathcal{V}+\...
0
votes
0answers
40 views

Inverting a lengthy matrix

I have a rather lengthy 10X10 matrix that I want to invert it. The matrix reads: ...
0
votes
0answers
58 views

Reconstruct equation by given solution

How can I reconstruct equation, which solution is given by series $\frac{x^{x-2}}{x!}$? The reverse task is straightforward with Solve function. It seems pretty ...
-1
votes
1answer
62 views

Invert a series with coefficients depending on x

Let's say I have the equation: $\qquad (8x^{15}+4x^{14}+\ldots)G^9 + (3x^{3}+\ldots)G^{8} + \ldots + (5x+4)G + x = x$. $G$ is an infinite series of $x$. I want to find the first 10 coefficients of $...