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.
43
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optimize this python code that involves matrix inversion
So I have this line of code that involves a matrix inversion
X = A @ B @ np.linalg.pinv(S)
$A$ is an $n$ by $n$ matrix, $B$ is an $n$ by $m$ matrix and $S$ is an $...
- 127
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1
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Approximately, at any given time, what proportion of the world's total HPC resources are dedicated towards inverting matrices?
I had heard in a lecture, perhaps 15 years ago, that the vast majority of the world's HPC resources were dedicated to solving linear systems by iterative methods. I seem to remember it was 90%. I can'...
- 31
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What algorithm(s) do numpy and scipy use to calculate matrix inverses?
I am solving differential equations that require inverting dense square matrices, and I wanted to know what algorithm(s) do numpy and scipy use to calculate matrix inverses?
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Why is matrix inversion unstable when svd is stable?
I've heard that matrix is inversion is unstable whereas the SVD is stable.
Now, if $A$ is an invertible matrix, then its SVD is
$$
A = USV^T
$$
Then wouldn't it's inverse just be
$$
A^{-1} = (USV^T)^{...
- 760
4
votes
1
answer
186
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The error propagation in calculating the inverse using a matrix decomposition
I have been trying to calculate the matrix inverse of some large matrix with entries ranging by orders of magnitude. I tried to use the matrix decomposition to simplify the computation, where a matrix
...
3
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1
answer
99
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SVD testing non zero values
I was looking at the matlab function pinv.m for the compuation of the pseudoinverse. The code uses the singular values decomposition.
$$
A = U D V
$$
When looking for non-zero diagonal elements it ...
- 153
2
votes
0
answers
245
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Numerical instability in the inverse Laplace transform
I have a problem with Laplace inversion and my function is not numerically stable for the Laplace inverse, but I do not understand the cause of this problem.
Here is my code and graph of this problem. ...
- 31
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1
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605
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MATLAB : find an algorithm to inverse quickly a large matrix of symbolic variables
I have to solve the equality between 2 matrixes 12x12 containing a lot of symbolic variables and with which I perform inversion of matrix. There is only one unknown called "...
user14831
2
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1
answer
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How to Invert a Poorly Conditioned Matrix
In my research, I need to invert a Fisher matrix in order to get a covariance matrix for me to do parameter estimation. Unfortunately, the values of Fisher matrix vary by many orders of magnitude, and ...
1
vote
0
answers
468
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Optimize speed for calculating the approximate inverse of a large matrix
I am searching for a faster method to calculate an approximate inverse of a large matrix (up to 32000x32000) resulting from a discrete non-linear system of partial differential equations. I'm using C++...
- 11
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Inverse of ill-conditioned symmetric matrix
I've got a matrix K, with dimensions $(n, n)$ where each element is computed using the following equation:
$$K_{i, j} = \exp(-\alpha t_i^2 -\gamma(t_i - t_j)^2 - \...
- 143
5
votes
1
answer
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approximate function such that the inverse of the approximation is "simple"
I have a smooth enough injective function $f:[a, b]\to \mathbb{R}$ which I want to approximate by something that can be computed quickly, e.g., a Padé approximant of low degree,
$$
\frac{\sum_{j=0}^m ...
- 3,136
5
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1
answer
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Fast algorithm for computing cofactor matrix
I wonder if there is a fast algorithm, say ($\mathcal O(n^3)$) for computing the cofactor matrix (or conjugate matrix) of an $N\times N$ square matrix. And yes, one could first compute its determinant ...
- 53
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Accurate way of getting the square root inverse of a positive definite symmetric matrix
What is the most accurate algorithm to get the square root inverse of a positive definite symmetric matrix? I am not looking as much for efficiency, though using quadruple precision computation is out ...
- 141
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Which pseudo-inverse to compute when Inverse is not possible? (No linear solve)
Let us assume that we have a function, $f(A)=\text{vec}(A^{-1})^\intercal B$, dependent on $A^{-1}$. However, due to some machine-precision limitations, the programming language I'm using cannot ...
