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Questions tagged [inverse]

For questions about computationally inverting a function/matrix/operation. The inverse "undoes" the action of the original operation, for example in the context of solving linear systems or differential equations.

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Updating matrix diagonal with Woodbury matrix identity and maintaining numerical accuracy

I have a dense matrix A and its corresponding inverse $A^{-1}$. The Woodbury matrix identity states: $$ (A + UCV)^{-1} = A^{-1} - A^{-1}U(C^{-1} + VA^{-1}U)^{-1}VA^{-1} $$ I wish to perform small ...
Costis's user avatar
  • 1,320
8 votes
0 answers
800 views

What is the source of the error in the Sherman-Morrison formula application?

The Sherman-Morrison formula $$ (A+uv^T)^{-1} = A^{-1} - \frac{A^{-1}uv^TA^{-1}}{1+v^TA^{-1}u} $$ results in small errors in relation to the standard matrix inverse operation after each application, ...
rcpinto's user avatar
  • 180
3 votes
0 answers
62 views

Dominant contributions of a quadratic form

Let $\Sigma$ be a covariance matrix (e.g. symmetric positive definite). For arbitrary vectors $\epsilon$, I need to compute $\chi^2 \equiv \epsilon^\top\Sigma^{-1}\epsilon$, which I do using a ...
yannick's user avatar
  • 375
2 votes
0 answers
229 views

Numerical instability in the inverse Laplace transform

I have a problem with Laplace inversion and my function is not numerically stable for the Laplace inverse, but I do not understand the cause of this problem. Here is my code and graph of this problem. ...
Ali AlCapone's user avatar
2 votes
0 answers
57 views

Inverted value is not consistent with expectation

We have a group of observations $$y = f(x_1, x_2, x_3) \enspace .$$ We have also a forward model $y = f(x_1, x_2)$. The forward model does not include $x_3$ because $x_3$ might include dozens of ...
Ting Yang's user avatar
1 vote
0 answers
457 views

Optimize speed for calculating the approximate inverse of a large matrix

I am searching for a faster method to calculate an approximate inverse of a large matrix (up to 32000x32000) resulting from a discrete non-linear system of partial differential equations. I'm using C++...
enco909's user avatar
  • 11
1 vote
0 answers
92 views

How to fast estimate derivates for calculating quantiles

I would like to know if there exists a package or how one can fast calculate the quantiles of a function within python, where the inverse of the function for calculating the quantile depends on the ...
math's user avatar
  • 101
1 vote
0 answers
133 views

Problem in analyzing the program of Gauss Jordan Inverse problem

I had to code a program which calculates Inverse of a matrix by Gauss-Jordan Inverse method , I was trying to analyse the program and then code it myself. the link http://hullooo.blogspot.in/2011/...
BAYMAX's user avatar
  • 229
1 vote
0 answers
48 views

Numerically inverting an exponentially growing function (defined by Chebyshev polynomials)

Assume a function $M(t)$ strictly increasing, essentially growing exponentially, and asymptoptically growing at a known rate $\bar{g}$, i.e. $\lim_{t\to\infty}M'(t)/M(t) = \bar{g}$ In a set of awful ...
jlperla's user avatar
  • 376
1 vote
0 answers
197 views

Efficient way to do congruent transformation using matrix inverse?

I know a square self-adjoint matrix $S_{vv}$ and I want to find: $S_{rr} = HS_{vv}H^{\dagger}$ where $\dagger$ denotes conjugate transpose. I do not know $H$ but I do know $H^{-1}$. What is the ...
James's user avatar
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