Matrix is a rectangular array of elements (e.q. numbers, symbols, or expressions), arranged in columns and rows.

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How to solve singular non symmetric poisson equation with Neumann boundary condtions?

I am trying to solve 2D Poisson equations with Neumann boundary conditions. When the mesh is uniform, Poisson equation is singular and symmetric, so the method listed in Null Space Projection for ...
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27 views

Given a 3x3 matrix, how to convert it into desired form with elementary row transforms?

Suppose matrix $A\in \mathbb{R}^{3\times 3}$ and rank($A$)=2; if $$A= \left( \begin{array}{c} a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\\ \end{array} ...
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1answer
34 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). ...
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1answer
82 views

Sparse matrix - matrix multiplication

How can a sparse matrix - matrix product be calculated? I know the 'classic' / mathematical way of doing it, but it seems pretty inefficient. I thought about storing the first matrix in CSR form and ...
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1answer
56 views

Gilbert-Peierls algorithm for LU Decomposition

I searched for Gilbert-Peierls algorithm, but I haven't found anything useful (well, I found this, but it's not working as it should). I think the problem is the second part, and also that those ...
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0answers
119 views

Givens method for sparse matrix

I have a (very) large sparse matrix in CSC form and I'm supposed to factorize it. I've read that between Givens and Householder transformations, Givens is better for a sparse matrix. The problem is ...
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2answers
96 views

Finding eigenvalues of a complex symmetric tridiagonal matrix

I am trying to find specific eigenvalues and -vectors of a large complex symmetric tridiagonal matrix (at least 10000x10000, and ideally larger). I know roughly which eigenvalues I am looking for, so ...
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2answers
75 views

What to do with singular (non-invertible) rotation matrix

I have an orthotropic material with a (6x1) stress vector known in the global coordinate system and yield surfaces known in a local coordinate system. So far I have only needed to convert from local ...
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29 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 ...
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1answer
87 views

Updating an approximate solution to a linear system in response to a small change

This question was original posted on SO but it was suggested that I post it here. I'm working on a program in which I have a banded matrix M and a vector b, and I want to maintain an approximate ...
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21 views

Markowitz Pivoting to reduce size of a dense integer system

I am dealing with a large sparse integer matrix that I need to find the nullspace of. I've seen Markowitz Pivoting come up in several places discussing similar problems such as here: ...
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76 views

Is it possible to construct such a symmetric matrix with desired eigenvalues?

Suppose a real, dense and asymmetric square matrix $A\in\mathbb{R}^{n\times n}$, all its eigenvalues $\lambda_i \in \mathbb R$ Is it possible to construct a symmetric matrix $B\in\mathbb{R}^{n\times ...
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19 views

MLLL algorithm for sparse, integer bases to find a nullspace

I am trying to find a suitable algorithm that can find a basis for the nullspace of a sparse, integer matrix. Reading A Course in Computational Algebraic Number Theory by Cohen, an algorithm based ...
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1answer
111 views

Nullspace algorithm for a sparse matrix

I am dealing with large, sparse, rational matrices that I need to determine the nullspace of. Currently, I have one that is about 12000x12000 (but not square), where one in every 2000ish elements is ...
3
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1answer
77 views

What is the most efficient way to obtain the max eigenvalue of a specific symmetric matrix via Eigen C++

Suppose I have a symmetric matrix $A_{1000\times 1000}$, which can be represented by: $A = J G J^T$ where $J$ in 1000x3 is full column rank dense matrix; $G$ in 3x3 is a nonsingular dense matrix. ...
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3answers
91 views

R/C/C++ library for N-dimensional arrays

I'm looking for a library that is either in R or easily wrappable with R, that can do the following things: construct and subset N-dimensional arrays perform operations such as ...
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2answers
113 views

Inverting a pressure matrix for fluid simulation

I am implementing a fluid simulator as my numerical methods course project and I have to compute pressure at each simulation step. Basically, that means solving an equation $Ap = b$, where $A$ is a ...
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1answer
69 views

What is the more than 3rd order Taylor series approximation for a multi-variate function?

Suppose $f$ is a infinite continuously differentiable map: $R^n\to R$, and $x,x_0 \in R^n$, then we have the following second order Taylor expansion of $f(x)$ at $x_0$: $$f(x)\approx ...
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58 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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121 views

How to prove the 2-norm of an invertible matrix is exactly the reciprocal of its minimum singular value?

If a matrix $A_{n\times n}$ is invertible, then $\left\|A^{-1}\right\|_2 = \dfrac{1}{\min\limits_{i} \sigma_i}$ where $\sigma_i$ is the $i$-th singular value of $A$
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3answers
81 views

Real eigenvalues finding

I have a question about matrix diagonalization. I don't know if this is the right forum... Is there a way to compute the smallest real eigenvalue (and eigenvector if possible) of a general real nxn ...
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1answer
66 views

Is slicing matrix a view or copy in cvxopt?

It is known that Numpy basic matrix slicing will generate a view, whereas advanced slicing a copy. Is this true in cvxopt? I tried ...
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1answer
364 views

Efficient computation of the matrix square root inverse

A common problem in statistics is computing the square root inverse of a symmetric positive definite matrix. What would be the most efficient way of computing this? I came across some literature ...
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1answer
111 views

Factorization for reweighted least squares

I am solving a problem using an iteratively-reweighted least squares method: http://en.wikipedia.org/wiki/Iteratively_reweighted_least_squares Essentially this requires solving a number of ...
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2answers
136 views

About Subspace Iteration for Eigenvalues

I heard that subspace iteration plus Ritz acceleration could improve the performance a lot for solving clustered eigenvalues, for the eigenvalues and eigenvectors could converge linearly with ratio ...
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1answer
66 views

How to change the dimensions of an Eigen Matrix in a loop?

I have a while loop, in which I use a Matrix A, vectors B and x with varying dimensions: ...
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1answer
125 views

Linear Algebra / Numerical Solution Of Matrix With Nullspace

I have a question relating to linear algebra. We have a fluid solver that solves the poisson equation for pressures. When there are areas of the domain that are entirely enclosed by Neumann ...
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2answers
261 views

Fast algorithm for Polar Decomposition

As it known, according to the Polar Decomposition, square matrix can be expressed in the next form $$M=QR$$ ($Q$ - othogonal matrix R - positive-semidefinite Hermitian matrix) I need to find this ...
3
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1answer
112 views

A programming model for Quantum Mechanics angular momenta in Mathematica

I'm writing prototypes for solving the Liouville Equations with Mathematica and C++. Perhaps the question about this may not be suited for this forum in a strict way, but it suits the people here ...
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2answers
227 views

Big matrix multiplication on single machine

For example I have 2 matrices that can't fit in RAM. I need algorithm or library which can handle this.Preferably Matlab or Python. I think it can be some block matrix multiplication? Also I think ...
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1answer
176 views

Why SVD is talk about less than QR and LU for sparse matrix?

For example the C++ sparse matrix libraries I used -- Eigen and SuiteSparse, they seem not to have any SVD funcitionality for sparse matrix. So just curious, is SVD more difficult than QR/LU for ...
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20 views

how to compute Rf(:,1:mi2)/Ru as like in Matlab

How to do Rf(:,1:mi2)/Ru ? it is like division, when i use Rf*inv(Ru), as Ru is not square matrix, i can not inv it would like to do this in c# or F# in Matlab, it is doing as below ...
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2answers
91 views

Computational complexity and implementation of UDU Modified Cholesky Rank 1 Update

I am attempting to increase the performance of a legacy Kalman Filter implementation. The state covariance is factored in terms of UDU, i.e. $\mathbf{P} = \mathbf{U}\mathbf{D}\mathbf{U}^T$. Many ...
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4answers
133 views

Are there any quad-double arithmetic sparse matrix package?

I am working on some ill-conditioned large sparse linear system of equations. I want to use double-double arithmetic or quad-double arithmetic to solve them. I know that there is a package named MPACK ...
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4answers
289 views

Library that performs sparse matrix-vector and matrix-transpose-vector multiplication

My main interest is sparse matrix-vector and matrix-transpose-vector multiplication of the form y=y+AA'x. Is there any library that performs ...
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2answers
299 views

debugging a rotation matrix for elastic constants

So the problem is that I have a transformation matrix which takes in the elastic constants from the local rtl coordinates and then converts the elastic constants to the global xyz coordinates via a ...
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3answers
124 views

Smoothly varying dense matrices arising from computational science

I have written an algorithm to solve a dense system with smoothly varying entries. This means I assume there is no large jump from any entry to its neighbors. I would love to use ...
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2answers
173 views

How can you calculate percent error in tensor approximations?

I have a matrix A which is an approximation to the known matrix B. Both matrices are square, 3x3 matrices and, in this case, are ...
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3answers
252 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?
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1answer
57 views

Extract clusters from a graph of absolute-distance edge

I don't know if I have formulated this problem right: I have tons of items and the distances between each pair of them. Feeding this data into some visualization tool, I am able to create a nice ...
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1answer
158 views

lapack singular matrix

I'd like to find a condition that allows me to determine if a matrix is invertible or not. naively, I computed the determinant to see if it was zero. but then I realized that even for very small ...
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2answers
133 views

lapack dorgqr qr decomposition matrix $m\times n$ with $m<n$

I'd like to do a $A=QR$ decomposition of a matrix $A$, with $m\times n$. I use dgeqrf_ (or dgeqp3_) to proceed to the first part ...
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2answers
164 views

find a set of linearly independent columns in a $m\times n$ matrix

my question is between mathematics, physics and informatics. Suppose i have an Hamiltonian (hermitian matrix) that i can diagonalize. The matrix that allows this transformation is a unitary matrix ...
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1answer
58 views

How to do transpose for trtrs (or tptrs) in blas?

How to do transpose for trtrs (or tptrs) in blas? I want to solve: XA = B But it seems that trtrs only lets me solve: ...
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1answer
521 views

generalized eigenvalue problem

I need to solve a real generalized eigenvalue problem $Ax= \lambda Bx(*)$ A and B are calculated from equations below: $$A=\sum_{i,j=1}^{N}W_{ij}(K_{i}-K_{j})\beta\beta^{T}(K_{i}-K_{j})^{T}$$ ...
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1answer
297 views

Finite Element, NASTRAN, DMAP, how to print the differential stiffness matrix in .f06 output file

We are working on an optimization problem in which we can approximate the eigenvalue calculation by assuming a constant eigenvector, using the formula: $$ ...
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1answer
233 views

matlab set center of output figure to [0 0 0]

I have a few set of data of three dimensional matrices, n x 3 with x, y and z coordinates. I viewed the matrices in the figure window. ...
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781 views

how can a 2-d fft be constructed to an equivalent matrix?

When I use the cvx matlab toolbox, I met a puzzled problem. The function of fft (or dct, wavelet, etc.) cannot be recognized by the type of 'cvx'. For the 1-d fft, it can be constructed to an ...
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2answers
1k views

Matlab element within ranges and distance between two points

I have a 53534x3 matrix with x, y and z coordinates. I want to find the element of matrix within ranges as follows: ...
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99 views

ZGETRF and ZGETRS from MKL - zgetrf fails and still zgetrs works?

please can you help me with my MKL problem? I have a big matrix - system of equations, so I have the linear problem Ax=b and I know the A matrix and b vector. I'm using MKL to solve this system. The ...