Questions tagged [matrix]

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

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

I want to invert large matrices ($10^4 \times 10^4$ to $10^6 \times 10^6$) but sparse (less than $100$ non-zero entries per line) on clusters with $16$ to $48$ processors per node. I'm looking for an ...
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Is there an efficient $O(n^2)$ way to estimate in MATLAB a matrix condition number given its LDL decomposition?

Since evaluating a matrix condition number usually takes $O(n^3)$, I wonder whether there is an efficient $O(n^2)$ way to estimate in MATLAB a matrix condition number given its LDL decomposition. ...
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Recommendation for C/C++ library which offers Schur complement functions?

I need to find C/C++ libraries which offer function for computing Schur complement. I know about MUMPS and Pastix, but I need more of them to compare them in my research. Do you have any experience ...
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Evaluating a quadratic form with an inverse of a sparse PD matrix, comparison between using the inverse vs using a Cholseky decomposition

I have the following quadratic form I need to evaluate: $x^T A^{-1} y$, where $A$ is a sparse positive definite matrix, $x, y$ are sparse vectors. Now assume that I am given for free both $A^{-1}$ ...
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SVD of large block-hankel matrix

I am trying to do SVD of a large block-hankel matrix for model order reduction (Low rank approximation). However, I quickly run into memory issues in forming the large Block-Hankel matrix and CPU ...
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$AX=B$: 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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I need to calculate a determinant consisting of vectors, using the Kronecker product as product. As an example I would need to be able to calculate: $\left| \begin{array}{cc} \left(\begin{array}{c}1\\... 1answer 141 views Simple way to derive transpose of a vectorized operation In a program I'm writing, I have a sub-routine that does some vectorized linear operations (specifically differentiation). Say for convenience I have defined the following inline function, which ... 1answer 1k views Difference between eigendecomposition and singular value decomposition for Hermitian matrices Let consider the following Hermitian matrix ... 1answer 163 views Solve eigenvalue problem using finite differences without vectorization I am interested in solving the problem$-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$is there to impose some ... 0answers 142 views How big a matrix can we row reduce in reasonable time? I have very large matrices that I would like to row reduce (I need to keep track of the steps and find a basis of the kernel/image, not just find the rank). The good news is that I work mod 2 and the ... 1answer 678 views What is a good way to take fractional powers of a matrix in MATLAB? I am working on a problem that involves taking fractional powers of particular matrices. For the matrix A with 2 on the main diagonal and -1 on the sub and super diagonal (the finite difference ... 1answer 2k views Why is my MATLAB code for back-substitution slower than the backslash operator? I wrote the code below to invert an upper triangular matrix, avoiding any possible multiplication/subtraction by zero. It just uses$\frac{1}{6}n^3+\ldots$flops instead of$n^3+\ldots$flops. ... 0answers 332 views Optimizing rank computation for very large sparse matrices I have a sparse matrix such as ... 0answers 89 views smallest eigenvalues for linear elasticity I want to compute a few tens of the smallest eigenvalues of a linear system which is a discretization of a linear elasticity. In the presence of additional constraints like Dirichlet boundary ... 2answers 516 views Are there any popular (paralleled) implementations of Lanczos methods for SVD/eigendecomposion? I want to use it in Matlab or Java. Will these two languages be much slower for computing the algorithm compared to C, C++, in case efficiency is an important factor? I'm aware of that there's a ... 1answer 194 views Can anyone give me some suggestions about optimize my Matlab codes? recently, I try to write a Matlab codes to implement a sparse approximation inverse factorization method proposed by M. Benzi in his paper http://www.mathcs.emory.edu/~benzi/Web_papers/ainv.pdf this ... 1answer 110 views Are there any algorithms “incrementally remove part of data (esp., old data)” from the existing SVD model of a data? Sometimes it is meaningful to remove the influence of some old data from a SVD-based model, so as to reflect the most updated trends and provide more accurate results. I've seen there're incremental ... 3answers 2k views Minimize quadratic form with equality constraints I want to minimize function:$f(x) = x^T \cdot A \cdot x + b \cdot x$given constraints:$B \cdot x = 0$. Here:$x$is a vector ($x \in \mathbb{R}^n$),$A$is a matrix of size$n \times n$,$b$... 2answers 610 views Get symmetric Finite Difference matrix in non Laplacian settings I would like to solve a system of differential equations$u+\nabla(\nabla\cdot u)=f$or in more detail$a+\partial_t^2a+\partial_t\partial_xb+\partial_t\partial_yc=fb+\partial_x^2b+\partial_x\...
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 \$B\in\...