# Questions tagged [linear-algebra]

Questions on the algorithmic/computational aspects of linear algebra, including the solution of linear systems, least squares problems, eigenproblems, and other such matters.

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### Estimation of condition numbers for very large matrices

Which approaches are used in practice for estimating the condition number of large sparse matrices?
132k views

### Recommendations for a usable, fast C++ matrix library?

Does anyone have recommendations on a usable, fast C++ matrix library? What I mean by usable is the following: Matrix objects have an intuitive interface (ex.: I can use rows and columns while ...
549 views

### What should be the criteria for accepting/rejecting singular values?

I am solving a system using singular value decomposition. The singular values (before scaling) are: ...
204 views

### Is there one general approach to build a projection methods for different problems?

My question is probably going to be too general to answer it with a couple words. Could you please suggest a good reading in that case. Projection methods are used to reduce size of the solution space ...
382 views

### In what application cases are additive preconditioning schemes superior to multiplicative ones?

In both domain decomposition (DD) and multigrid (MG) methods, one may compose the application of the block updates or coarse corrections as either additive or multiplicative. For pointwise solvers, ...
895 views

### Linear regression via SVD not producing best fit with escalating polynomial degree

I am using a basic singular value decomposition (via LAPACK) routine in FORTRAN to solve an overdetermined system in the form of $A\cdot X = B$ where $\mathrm{size}(A) = [m,n]$ with $m > n$. My ...
14k views

### Performance differences between ATLAS and MKL?

ATLAS is a free BLAS/LAPACK replacement that tunes itself to the machine when compiled. MKL is the commercial library shipped by Intel. Are these two libraries comparable when it comes to performance, ...
1k views

### How can I compute the Schur complement in PETSc?

How can I compute the Schur complement: $$S = K_{bb} - K_{ba} K_{aa}^{-1} K_{ab}$$ where $$K=\begin{pmatrix} K_{aa} & K_{ab} \\ K_{ba} & K_{bb} \end{pmatrix}$$ (in some ordering) is a ...
2k views

### Why is my parallel solver slower than my sequential solver?

I was playing around with PETSc and noticed that when I run my program with more than one process via MPI it seems to run even slower! How can I check to see what is going on?
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### Efficient tridiagonal matrix algorithm implementation

I am solving a physical problem using implicit numerical scheme. This leads me to solving a linear equation with tridiagonal matrix. I've coded this algorithm from Wikipedia. I wonder if there is an ...
10k views

### Libraries for solving sparse linear systems

There are a number of different libraries out there that solve a sparse linear system of equations, however I'm finding it difficult to figure out what the differences are. As far as I can tell there ...