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1
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1answer
73 views

Efficient methods to solve large dense singular least square problem (linear system)

I am trying to solve a singular linear least square problem: $$minimize: \phantom{2} ||Ax-b||^2 \\ subject \phantom{2} to: \phantom{2} x \ge 0$$ Here $ A \in R^{n \times m} $, and $ n\lt m$. here m ...
0
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1answer
107 views

Solve a very large linear system (question about a library linear algebra to do this)

I need to solve a very large linear system (coming from finite element method). I'm currently using the Intel MKL library, but the system has been delayed more than 20 hours. The matrix of the system ...
3
votes
2answers
157 views

Solving a system of linear equations with only an approximate solution

I have a system of linear equations that is derived partially from experimental data. Theoretically, the system should have a single, exact solution; however, experimental error causes it to not have ...
3
votes
1answer
83 views

Solve rank one update to LU using plain vanilla LU routine

I have a large number of systems of the form: $$A_ix=b,$$ where each $A_i,i>0$ is a rank one update of $A_{i-1}$ and the $A_i$ are dense matrices. I was wondering whether it is possible to use the ...
1
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0answers
62 views

Block preconditioners and condition number

I am working with block Jacobi like preconditioners which are very cheap for my problem. But I could not find much about the dynamics of basic preconditioners (block Jacobi, Gauss-Seidel, ILU etc). ...
3
votes
5answers
276 views

Speed of solving linear system with block diagonal matrix

I have a bunch of 3x3 linear systems of the form $Ax=b$. In general, would it be faster to solve each individual system, or to formulate it as a giant block diagonal system and solve that? I expect ...
3
votes
1answer
224 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 $a+\partial_t^2a+\partial_t\partial_xb+\partial_t\partial_yc=f$ ...
5
votes
1answer
175 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 ...
4
votes
2answers
125 views

Solving “Hadamard systems”

Suppose we have two matrices $A$ and $B$ (we can assume they're symmetric; if absolutely necessary I think they may be positive definite). Then, is there any technique for solving $$(A\circ B)x=b,$$ ...
3
votes
1answer
495 views

solving a linearly-constrained sparse linear least-squares problem

[ question reposted from http://math.stackexchange.com/questions/786612/solving-a-linearly-constrained-sparse-linear-least-squares-problem ] Given the system of equations $Ax=b$, subject to $Cx\le ...
4
votes
2answers
212 views

Methods for solving linear systems

This is such a basic topic but there are so many different methods proposed for solving a linear system of equations. I recently found a very good source but couldn't really make sense of all the ...
7
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3answers
1k views

Sort of problems where SOR is faster than Gauss-Seidel?

Is there any simple rule of thumb to say if it is worth to do SOR instead of Gauss-Seidel? ( and possible way how to estimate realxation parameter $\omega$) I mean just by looking on the matrix, or ...
7
votes
0answers
187 views

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 ...
1
vote
2answers
901 views

Vortex Panel Method implementation

I'm trying to understand and implement panel methods for a two-dimensional airfoil. I haven't found yet a very detailed explanation on how to implement it, and there are some things I don't' still ...
2
votes
1answer
155 views

SPD matrices with right hand sides

I'm looking for sparse SPD matrices with right hand side? There is UF collection of sparse matrices , however, I'm not sure how do I search of the matrices of these kind efficiently ( I'm doing a ...
7
votes
5answers
4k views

Best choice of solver for a large sparse symmetric (but not positive definite) system

I am presently working on solving very large symmetric (but not positive definite) systems, generated by some certain algorithms. These matrices have a nice block sparsity which can be used for ...
4
votes
3answers
297 views

PRIMA gives an unstable result?

I am working with Modified Nodal Admittance representation of circuits. I am doing Model Order Reduction using PRIMA on MATLAB. I am considering these circuits as Descriptor State-Space systems. I ...
10
votes
1answer
338 views

Solving huge dense linear system?

Is there any hope in solving the following linear system efficiently with an iterative method? $A \in \mathbb{R}^{n \times n}, x \in \mathbb{R}^n, b \in \mathbb{R}^n \text{, with } n > 10^6$ ...
5
votes
2answers
623 views

Largest invertible dense matrix with standard solvers such as Lapack

I have a matrix which is complex symmetric. It is around 50,000 elements per side. It is a Method of Moments matrix. Is it feasible to use a standard direct solver such as Lapack to do a matrix ...