# Questions tagged [matrix]

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

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### Wanted: sequences of linear systems for recycling Krylov solver analysis

In the solution of sequences of linear systems $$A_ix_i=b_i\quad\text{for}\quad i=1,2,\dots$$ with Krylov subspace methods, data can be recycled from already solved linear systems in order to speed up ...
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### 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 ...
382 views

### Speed and accuracy of Strassen vs Winograd matrix multiplication algorithms

I am doing work which requires as fast matrix multiplication as possible and just want to double-check with this community that the Winograd variant of Strassen's MM algorithm is the fastest practical ...
356 views

### Eigenvalue with largest imaginary part

Iterative eigensolvers such as ARPACK, give the option to find a subset of the eigenvalues which have the largest imaginary part. My question is how do these algorithms work. As I understand it, ...
600 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, ...
179 views

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### Hessian eigenvalues in 4D-VAR data assimilation

I am using variational data assimilation (4D-VAR) to estimate emissions of anthropogenic greenhouse gases using a rather complex atmospheric transport model. Hence, the optimal solution to my problem ...
765 views

### Does it matter if I use principal component analysis on the transpose instead of the original matrix?

My data set is a 60x10 matrix. I performed principal component analysis of this matrix with matlab using the princomp(AdjustedData) after I adjusting my original data set by subtracting the mean of ...
994 views

### 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 ...