Newest 'inverse' Questions

1

vote

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Matlab - Equality between 2 Fisher matrices constructed in a different way

I want to know if, on a Fisher matrix, the projection operation (with a Jacobian matrix) commutes with a matricial inversion operation. The 2 ways to build these 2 matrices are: 1) First method: 1.1) ...

asked Jul 19 '21 at 18:12

youpilat13

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vote

1answer

225 views

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 "...

matlab matrix gpu inverse matrix-equations

asked Apr 23 '21 at 12:53

youpilat13

518 bronze badges

2

votes

1answer

221 views

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 ...

matrix numpy condition-number inverse

asked Jan 22 '21 at 7:22

Brian.C.Seymour

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vote

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223 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++...

nonlinear-equations c++ inverse eigen

asked Nov 14 '20 at 11:25

enco909

113 bronze badges

4

votes

3answers

753 views

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 - \...

matrix precision inverse

asked Oct 1 '19 at 23:11

adityar

1435 bronze badges

5

votes

1answer

74 views

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 ...

approximation inverse

asked Sep 2 '19 at 8:18

Nico Schlömer

3,04814 silver badges34 bronze badges

5

votes

1answer

783 views

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 ...

linear-algebra matrix algorithms inverse

asked Jul 9 '19 at 9:52

ZUN LI

533 bronze badges

4

votes

1answer

350 views

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 ...

linear-algebra matrix numerics inverse

asked Jun 1 '19 at 18:55

Javier Garcia

1414 bronze badges

2

votes

1answer

99 views

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 ...

linear-algebra inverse

asked Apr 26 '19 at 21:50

An old man in the sea.

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vote

1answer

3k views

Computing the Inverse of a matrix, using the Cholesky decomposition

I have to compute $CA^{-1}B$ and $CA^{-1}x$, where $A,B,C$ are conformable matrices and $x$ is a vector. I've read that the a very computationally stable way to compute these inverses is by computing ...

linear-algebra inverse

asked Jan 14 '19 at 18:04

An old man in the sea.

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2

votes

1answer

92 views

Inverting small matrices: canned factorization versus explicit formula

I am interested in solving a large number of small linear systems of equations, $Ax=b$, with $A$ either $2\times2$ or $3\times3$. Assuming none of these systems are actually singular, is there ...

linear-algebra lapack inverse

asked Oct 16 '18 at 15:35

Endulum

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4

votes

1answer

191 views

Do I really need to invert this matrix

I need to calculate a matrix $A$ (at least some elements of it, see below) as defined by the following equation $$ A=B(\mathbb{1}-B)^{-1} $$ where B is a square matrix of dimension $N$ and $\mathbb{...

linear-algebra matrix inverse

asked Oct 13 '18 at 10:41

zakk

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7

votes

1answer

952 views

How to directly compute the inverse of an ill-conditioned dense matrix

I know that it is generally a bad idea to compute the inverse matrix directly. However, if it is necessary to compute the inverse of an ill-conditioned invertible dense matrix, then what can I try? ...

reference-request preconditioning condition-number inverse

asked Mar 21 '18 at 7:01

nekketsuuu

1736 bronze badges

4

votes

1answer

636 views

What is the fastest method to invert millions of matrices?

My project involves large simulation and estimation. For each simulation I need to solve 600,000 systems of nonlinear equations. Currently I am using Newton's method to find the solutions. That ...

matrix inverse jacobian

asked Mar 14 '18 at 17:03

THwang

433 bronze badges

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vote

0answers

84 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 ...

python inverse

asked Nov 10 '17 at 16:48

math

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1

vote

2answers

278 views

Inverting big symmetric and singular matrices

In this post I found a very similar probem to the one I have, but not a satisfactory answer for my purposes. I have a set of matrices $C_\ell$. They are exactly symmetric by construction. ...

matrix c++ svd inverse

asked Nov 7 '17 at 16:17

johnhenry

1292 bronze badges

0

votes

1answer

119 views

Sparse matrix inverse with reduced bandwidth

I have a sparse symmetric matrix of dimension 1393x1393 (8308 no zero elements), with bandwidth 1380. By Cuthill–McKee algorithm, I could achieve a new matrix with ...

sparse-matrix matrix r inverse

asked Jun 28 '17 at 20:55

Jiang Du

11 bronze badge

1

vote

0answers

126 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/...

numerical-analysis c++ matrix c inverse

asked Mar 21 '17 at 10:55

BAYMAX

2292 silver badges9 bronze badges

18

votes

2answers

2k views

Practical example of why it is not good to invert a matrix

I am aware about that inverting a matrix to solve a linear system is not a good idea, since it is not as accurate and as efficient as directly solving the system or using LU, Cholesky or QR ...

matrix accuracy inverse

asked Mar 17 '17 at 11:02

Manu

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vote

0answers

47 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 ...

inverse collocation chebyshev

asked Feb 4 '17 at 5:12

jlperla

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10

votes

1answer

492 views

The fast, and The Backward-Stable (left) $3\times 3$ matrix inverse

I need to compute a lot of $3\times3$ matrix inverses (for Newton iteration polar decomposition), with very small number of degenerate cases ($<0.1\%$). Explicit inverse (via matrix minors divided ...

matrix matrix-equations inverse matrix-factorization

asked Mar 5 '16 at 15:43

Sergiy Migdalskiy

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votes

1answer

219 views

Fast computation of square root inverse of matrix, matrix being determined from Ax=b form

I have an equation of the form $J^Te=f$, where $e$ and $f$ are known vectors and $J$ is an unknown matrix. How can I efficiently compute $J^T(JJ^T)^{-1/2}e$ ? My motivation to address this problem ...

linear-algebra matrix inverse matrix-free

asked Mar 5 '16 at 14:54

user3619023

111 bronze badge

1

vote

1answer

378 views

Calculate inverse of dense matrix with entries of very different magnitude

I need to calculate the inverse of a dense matrix, with some elements taking values as high as 1e9 and some around 1e2. What would be the best method to do it? Note: I am more concerned about the ...

linear-algebra stability inverse

asked Mar 4 '16 at 13:20

user3496912

133 bronze badges

13

votes

2answers

11k views

Complexity of matrix inversion in numpy

I am solving differential equations that require to invert dense square matrices. This matrix inversion consumes the most of my computation time, so I was wondering if I am using the fastest algorithm ...

numpy dense-matrix inverse

asked Feb 11 '16 at 15:05

physicsGuy

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4

votes

1answer

111 views

Finding the matrix inverse given a solver for the matrix equation $Ax=b$

So I'm given a solver that can solve for $x$ in the matrix equation $\underset{=}{A} \underline{x} = \underline{b}$ where $b$ can be anything we specify. (NB: A is an NxN matrix). I now want to find ...

matrix linear-solver inverse

asked Jan 9 '16 at 15:19

SomePhysicsStudent

1635 bronze badges

1

vote

2answers

161 views

Inverse of "diagonally not dominant matrix"

I want to frame a higher order Central difference scheme of about $20^{th}$ order for first derivative. I'm using $20^{th}$ order because I need one scheme with good modified wave number. To find the ...

numerical-analysis matrix inverse

asked Dec 13 '15 at 4:51

Arun Govind Neelan

5144 silver badges12 bronze badges

4

votes

1answer

470 views

Obtaining column vectors of pseudo-inverse of a matrix

I need to compute the pseudo-inverse of a very large rectangular dense matrix without any special structure or properties. I run out of memory/computing power and have no access to a large parallel ...

linear-algebra matlab matrix svd inverse

asked Oct 14 '15 at 9:17

Dr Krishnakumar Gopalakrishnan

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2

votes

0answers

52 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 ...

optimization constrained-optimization inverse-problem curve-fitting inverse

asked Aug 14 '15 at 19:53

Ting Yang

211 bronze badge

7

votes

0answers

627 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, ...

linear-algebra matrix stability inverse

asked Aug 6 '15 at 5:30

rcpinto

1704 bronze badges

3

votes

3answers

697 views

Exact analytical matrix inversion of sparse 100x100 matrices in C++

I need to invert a matrix. Of course, I'm not the first person in this situation, and I know that there's a wealth of powerful libraries out there, of which I only know a couple. That being said, ...

matrix computer-arithmetic inverse

asked Jul 1 '15 at 23:41

carsten

1335 bronze badges

6

votes

1answer

599 views

Is there a faster method to compute the geometric series of a matrix?

I want to calculate the geometric series of a matrix $A$: $$S=I+A+A^2+\dots+A^n$$ and then apply to a vector $v$, $Sv$. I've done it in Matlab with a loop and I think it's quite efficient applying ...

matlab matrix inverse

asked Feb 2 '15 at 11:00

jinawee

1715 bronze badges

1

vote

1answer

1k views

computing the inverse of a large block diagonal sparse matrix in r

I would like to compute the inverse of some large block diagonal sparse matrix. The number of rows and columns is somewhat over 50,000. The blocks are 12 by 12 and are sparse (27 non zero elements). ...

sparse-matrix matrix r inverse

asked Apr 6 '14 at 18:33

user3499209

213 bronze badges

3

votes

0answers

58 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 ...

eigensystem matrix inverse

asked Feb 25 '14 at 14:58

yannick

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1

vote

0answers

157 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 ...

linear-algebra matrix eigenvalues inverse matrix-factorization

asked Feb 11 '14 at 15:22

James

111 bronze badge

0

votes

2answers

455 views

closed form approximation of matrix inverse with special properties

I'm trying to find some theory to help me explicitly express the inverse of a matrix (or a close approximation of the inverse). My matrix has the following properties: invertible positive definite ...

matrix approximation inverse

asked Jan 20 '14 at 16:37

John

92 bronze badges

5

votes

2answers

822 views

Perturbation of Cholesky decomposition for matrix inversion

I am looking for a computationally cheap way to compute $x$ such that $$(L L^T + \mu^2 I)x = y$$ where $L \in \mathbb{R}^{n \times n}$ is a lower triangular definite positive matrix (with some very ...

linear-algebra matrix inverse

asked Jan 13 '14 at 18:03

Mathieu Galtier

512 bronze badges

9

votes

0answers

465 views

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 ...

matrix precision accuracy inverse

asked Dec 7 '13 at 14:26

Costis

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