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4
votes
0answers
91 views

Least-squares for a diagonal matrix

This is a follow-up to a different question I asked with more detail. For $v\in\mathbb{R}^n$, denote $D_v\in\mathbb{R}^n$ as the diagonal matrix with elements in $v$. Given a "tall" matrix ...
0
votes
0answers
35 views

Getting to a number as an addition of products (x*constant)

I have a list of constants and a list of targets. For each target, I want to find a set of probabilities (3-6 values != 0) such that the sum of constant^i * prob^i is close to the target. I get ...
0
votes
0answers
24 views

convergence of self-consistent solution- vector of large no. of points

I have a matrix equation $\left(\begin{array}{cc} \frac{\delta^{2}}{\delta x^{2}}+\mu & D(x)\\ D(x) & \frac{\delta^{2}}{\delta x^{2}}+\mu \end{array}\right)\left(\begin{array}{c} u(x)\\ v(x) ...
2
votes
1answer
92 views

SVD and HITS Algorithm Power Iterations

As we know, computing the authority (or hub) score of HITS ranking method, means to use the following matrix equation: $$ \textbf{a}^{k}=A^T A\textbf{a}^{(k-1)} $$ and apply the power iteration ...
0
votes
0answers
91 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 ...
1
vote
4answers
407 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. ...
1
vote
1answer
137 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 ...
3
votes
3answers
325 views

What is the best solver for solving a large sparse indefinite system

What's the best solver that can solve a large sparse but indefinite matrix?
2
votes
0answers
58 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
votes
1answer
90 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
votes
2answers
153 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 ...
9
votes
2answers
1k views

solve $xA=b$ for $x$ using LAPACK and BLAS

I am porting an existing code from MATLAB to C++ and have a linear system to solve $xA=b$ (rather than the more typical form $Ax=b$) The matrix $A$ is dense, and of general form, but is no larger ...
10
votes
5answers
432 views

Repeatedly solving $A\mathbf{x} = \mathbf{b}$ with same $A$, different $\mathbf{b}$

I am using MATLAB to solve a problem that involves solving $A\mathbf{x}=\mathbf{b}$ at every timestep ($\mathbf{b}$ changes with time). Right now I am accomplishing this by MATLAB's ...
3
votes
2answers
142 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
votes
3answers
333 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 ...