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-3
votes
0answers
44 views

How to find the inverse function of a function like f: N x N -> N [on hold]

I need help on how to find the inverse of a function N x N -> N For example, if anybody could give me a step by step explanation how to find the inverse function of f(x,y)=3x-2y I would be very ...
2
votes
0answers
174 views

How is the deconvolution of a fat gaussian from a polynomial derived?

We have a 2D order-2 polynomial, a Gaussian and a 'box' indicator function. Let: $\begin{eqnarray} p(x,y) &=& c_0+c_1x+c_2y+c_3xy+c_4x^2+c_5y^2+c_6xy^2 \\ G(x,y) &=& ...
2
votes
1answer
57 views

radius of the ball where the inverse of Lipschitz maps exists

I am aware of the inverse function theorem for Lipschitz maps, which uses the notion of generalised derivative $δ_{x_0} f$ of a Lipschitz map $f$, due to F.H.Clarke: Teorem. Let $f : U ⊂ \mathbb{R}^n ...
2
votes
1answer
91 views

Partial recovery from Radon transform

Let $f : \mathbb R^3 \to \mathbb R$ be an integrable function. Let $\eta$ be a one-dimensional subspace of $\mathbb R^3$. We denote $p+\eta$ the affine subspace (a line) which is obtained by ...
3
votes
0answers
87 views

Inverting a matrix with entries equal to positive or negative infinity

I would like to define an inverse on matrices whose entries may be positive or negative infinity. To formulate my problem precisely, suppose that I have a matrix $A$ and another matrix $B$. How do I ...
1
vote
1answer
89 views

Inverses of two-argument functions with respect to one argument

I asked a shorter version of this question at math.stackexchange.com four days ago but it hasn't gotten any answers or comments. Consider a function $f : A \times B \to C$ and two inverses, each with ...
1
vote
0answers
235 views

Update the inverse of sum of two symmetric matrices

There are two invertible symmetric matrices A and B, of which B is a block diagonal. A and B have the same dimensions. I need to iteratively calculate the inverse of M = s * A + B, where s is a ...
5
votes
0answers
118 views

Inverse problems for an asymptotic series which depends on a parameter?

I have the series $\sum_{n=0}^{\infty}(-1)^{n}a_{n}(\nu)\frac{\sin[\nu\,(m-n)]}{\nu\,(m^2-n^2)}=\frac{1}{m}$, where $m$ is an integer. Is it possible to compute the coeffients $a_{n}(\nu)$? An ...
2
votes
1answer
210 views

Non-linear 1st order difference equation

I have been trying to solve the following difference equation for some time now : $$u^3(n+1) = a - b\cdot u^2(n) + u^3(n), \qquad a \ne 0 \ne b$$ I have tried various substitutions, simplifications ...
5
votes
1answer
249 views

How to prove Lambert's W function is not elementary?

Liouville's theorem gives such a proof for antiderivatives of functions like $e^x/x$ or $e^{x^2}$, and differential Galois thory extends that to Bessel functions, say. But what tools exist for ...
0
votes
1answer
1k views

Derivative of log determinant and inverse.

Hi all I have a matrix $\Sigma$ with element $(i,j)$ $\Sigma_{i,j}= exp(-h_{i,j}\rho)$. The matrix is positive definite and symmetric (it is a covariance matrix). Now i need to evaluated ...
1
vote
0answers
108 views

bounds on the entries of an inverse circulant matrix

Suppose that $C$ is a (real) circulant invertible matrix defined by a vector $d$. Then $C^{-1}$ is also a circulant defined by some vector $f$. There exists a standard formula that expresses the ...
2
votes
0answers
257 views

Fast inversion of a special kind of matrices - approximations are ok

Suppose I have a stochastic matrix $M$ (with thousands or millions of stochastic column vectors), which I split into two matrices: $D$ containing only the diagonal entries of $M$, and $R$ containing ...
4
votes
1answer
2k views

How to calculate the inverse of the sum of an identity and a Kronecker product efficiently?

I have a matrix $K$ which is the sum of a identity and a Kronecker product of two symmetric matrices as following and I want to calculate the inverse of it $K^{-1}$. \begin{eqnarray} ...
1
vote
4answers
249 views

inverse-closed matrix spaces

Is there a known characterization of such spaces? An example: the space of $n \times n$ matrices spanned by $I$ and $J$ (the identity and all-ones matrices, respectively) is inverse closed by the ...
1
vote
1answer
292 views

sign-flipping inverse

Consider this matrix: $Z=\begin{bmatrix}23.9 & -7 & -17 \\\\ -7 & 23.9 & -17 \\\\ -17 & -17 & 33.9 \end{bmatrix}$ Its inverse is entrywise negative (you can check...) and ...