This question is about equations where the unknown itself is a matrix such as Sylvester or Riccati equations. For systems of linear equations (where the unknown is a vector), use "linear-system".

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38 views

Pivoting in Crout algorithm

Consider the following code, found on wikipedia, that implements the Crout decomposition algorithm: ...
7
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0answers
71 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 ...
2
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0answers
92 views

FLOPS of a linear system

I have two questions that I want to ask. Consider the following system: $$BM = A$$ i) $B$ is a $n$ by $n$ tridiagonal matrix and $A$ is a diagonal matrix. What is the leading order computation cost ...
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1answer
90 views

solve linear system of equation of a large sparse symetric positive definite matrix

I want to invert large matrices ($10^4x10^4$ to $10^6x10^6$) but sparce (less than 100 non-zero entries per line) on clusters with 16 to 48 processors per node. I'm looking for an efficient method to ...
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1answer
167 views

$AX=B$: How to solve for $X$ if elements of matrix A are matrices

Objective: I am trying to solve for $C$ in 2D space (x,y) and time from following PDE. $$ \text{PDE: }\frac{\partial C}{\partial t} + \nabla\left(v.C - D\nabla{C} \right)= \alpha.C $$ Method: I ...
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0answers
286 views

MATLAB: code for restarted gmres

I have a question about Matlab and restarted gmres. I would like to use gmres.m provided here. This code seems to be a popular for the scientific computation ...
0
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1answer
99 views

Avoid arithmetic overflow in matrix multiplication

I am solving the following matrix equation for $\mathbf{x}$: $$(J^{\mathbf{T}}J)\mathbf{x}=J^{\mathbf{T}}\mathbf{r}$$ $J$ is $m\times n$ matrix $\mathbf{x}$ is vector of size $n$ $\mathbf{r}$ is ...
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1answer
85 views

Solve eigenvalue problem using finite differences without vectorization

I am interested in solving the problem $-A u = \lambda u$ on a finite differences grid on a square. In my case, the operator $A$ is of the type $-\Delta + \mu I$, where $\mu$ is there to impose some ...
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0answers
148 views

How to find out if it is possible to contruct a binary matrix with given row and column sums

How to find out if it is possible to contruct a binary matrix with given row and column sums. Input : The first row of input contains two numbers 1≤m,n≤1000, the number of rows and columns of the ...
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4answers
1k views

Best PARALLEL numerical solver of first order differential equation

I have a system of 256 differential equations that I want to solve numerically. The system represents the Liouville equation, which is a first order, linear differential equation with complex numbers. ...
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1answer
249 views

PETSc: Blocking matrices using MatCreateSeqBAIJ and MatSetValuesBlocked

I am a little confused with PETSc's documentation for MatSetValuesBlocked. The code below works fine for matrices when I choose small block sizes, but I get errors ...
2
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0answers
71 views

On solution of a class of discrete-time Lyapunov equation for systems with multiplicaitve noise

Let's consider the following equation $$X=F_{1}XF_{1}^{T}+...+F_{p}XF_{p}^{T}+C$$ where $p$ is an positive integer and $C$ is a known positive semidefinite matrix. If we augment $F=[F_{1}...F_{p}]$ ...
2
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1answer
107 views

Calculate 3x3 matrix to give lowest difference for data set

I'm building an application where I need to compare found data with the actual data it should be. I have 5 sets of data, each with 3 variables a,b,c. Let matrix A be a 3x1 matrix with data a,b,c ...
6
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2answers
158 views

Left and right eigenspaces of the product of Gramians

I solve the Lyapunov equations : $$ A W_C E^T + E W_C A^T + B B^T = 0 $$ $$ A^T W_O E^T + E W_O A + C^T C = 0 $$ to obtain $ W_C $ and $W_O$. My aim is to get the left and right eigenspaces of $W_C ...
3
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2answers
173 views

Computing an orthogonal matrix subject to linear constraints

I am looking for a method to solve the matrix equation $$ DXa = Xb $$ where $D\in \mathbb{R}^{n\times n}$ is diagonal, $a, b\in \mathbb{R}^{n}$ and $X$ is the unknown orthogonal $n\times n$ matrix ...
9
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3answers
540 views

Libraries for solving Lyapunov's equation

The following matrix equation $$B\Sigma + \Sigma B^T + C = 0$$ in $\Sigma$ $-$ for given $B$ and $C$ matrices $-$ appears in my work as a characterization of a covariance matrix. I have learned that ...