# Questions tagged [sparse-matrix]

Questions related to storage, assembly, operations, and other aspects of dealing with sparse matrices, for which only non-zero elements are stored. Questions that do not with sparse matrices directly, but other means of using sparsity should be tagged with [sparse-operator].

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### Finding ALL Eingenvalues of a Sparse Integer Matrix

I would like to find ALL Eingenvalues of a huge, very sparse integer matrix. This matrix has a lot of known properties, e.g. that it is symmetric and nearly tridiagonal, with very few (max. ca. 4 per ...
88 views

### Eliminate variables from a large system of equations

I have a large system of equations $Ax=0$. For context, the equations are invariants of some model. $A$ is sparse and typically has more columns than rows ($m < n$). The $x$ vector can be divided ...
• 31
101 views

### Iterative solvers for problems in solid and structural mechanics

I am looking for comprehensive literature (papers, books, reports etc..) on iterative solvers for solid and structural mechanics problems to understand the best iterative solvers and preconditioners ...
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### How large is large for direct solvers?

Let us say I want to solve a large sparse linear system. It is said that iterative solvers should be better than direct solvers in this case. But how large is large? What is the exact threshold beyond ...
• 181
1 vote
76 views

### Fill-reducing ordering for computing the matrix product $A^T A$?

I have found many libraries for reducing filling when dong Cholesky factorisation on sparse matrices. However, I want to do fill-reduction for a different reason - given a $m\times n$ matrix $A,$ I ...
• 161
75 views

### Eigenvalue problem and pseudoinverse of a product of sparse matrices

If I have some dense matrix that can be decomposed into a product of sparse matrices with known(but different) sparsity patterns. Can I somehow use this information to more efficiently compute its ...
• 113
45 views

### using scipy.sparse.linalg.eigsh for degenerate states in Bose Hubbard model

I am currently writing a code for the Bose-Hubbard model, and I am calculating the ground states and single-particle density matrix for different values of U and J. As U=0, one would see how the ...
426 views

### How to leverage the GPU for parallel 3-body problem computations

I have a 3-body simulation which must run millions of times. As far as I know, the GPU shines when it gets to preform simple operations on huge matrices/arrays. Currently I'm debugging and running my ...
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### Solving $(I-Q)x={\bf 1}$ for sub-stochastic sparse $Q$ of dimension 5M $\times$ 5M

I have a (right) sub-stochastic CSC sparse matrix $Q$ of dimension 5 million, with 200 million nonzero entries, which is a nonzero percentage of 0.0008%, so it is indeed extremely sparse. It is not ...
• 503
136 views

### Fast Fourier Transform on Meshes

I have a (closed, manifold, oriented) triangular mesh for which I build a matrix $L\in\mathbb{R}^{n\times n}$ discretising the negated Laplace-Beltrami operator. The matrix $L$ is symmetric positive ...
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### Problems on the algebraic theory of sparse matrices

I have finished testing basic large densely parallel matrix multiplication on 4 gpu's ,and have done work on TSLU and TSQR on cpu's based on mpi. I am going to continue working on the theory of ...
237 views

### Right blocked linear equation solver on Dense Algebra and Sparse Algebra

I have implemented 1D mesh parallel QR decomposition and LU decomposition,I would like to ask if a linear equation Ax=b,b is a large matrix and I need to shard b or Shard A,b at the same time. Is ...
357 views

### How to efficient solve $e^{-tA} x =b$, where A is a very sparse matrix

I am going to solve an equation containing an exponential matrix $e^{tA} x =b$, which can be obtained naturally through $x=e^{-tA} b$. A is a 1million $\times$ 1 million matrix with stores 7.15 ...
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1 vote
194 views

### Are there good block sparse matrix solver libraries?

There are some great libraries with linear solvers for sparse matrices - SuiteSparse is the obvious one. The methods work on sparse matrices with scalar entries. However, often in optimization ...
• 111
87 views

### Diagonalization of large sparse matrix, computational programme recommendation and methods

According to this link, All eigenpairs of large sparse symmetric matrix. The guy @Baranas seems to have given a very confident answer about solving the whole Eigen spectrum. May I know if anyone has ...
260 views

### Solving Poisson's equation without a Dirichlet boundary condition

Some context of what I am trying to do: I am trying to implement a function that uses the heat method to calculate geodesic distances in a tetrahedral mesh, and I want to calculate the distances for ...
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104 views

### What is the difference between approximations of mixed derivative and how to implement it

currently I am solving 2D nonlinear second order differential equation containing mixed derivative. I started searching how to descretisize it and found two formulas for 4th order approximation. First ...
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381 views

### Accelerating the computation of scipy.sparse.linalg.expm_multiply

I have a tridiagonal antiHermitian matrix ($-i*Hami*t$) with nonzero elements only along the upper diagonal and lower diagonal, and the goal is to know the action of exponential of such matrix on a ...
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234 views

### How to efficiently fill in, in parallel, a PETSc matrix from a COO sparse matrix?

Considering the following COO sparse matrix format, with repeated indices: ...
1 vote
395 views

### Crank Nicolson Method with closed boundary conditions

I want to simulate 1D diffusion with a constant diffusion coefficient using the Crank-Nicolson method. $$\frac{\partial u (x,t)}{\partial t} = D \frac{\partial^2 u(x,t)}{\partial x^2}.$$ I take an ...
• 111
1 vote
54 views

### Assembling a sparse matrix for the PaStiX solver

I've been searching the whole afternoon for some documentation or code sample showing how to assemble a sparse matrix of a problem to be solved with PaStiX, but couldn't find any. The relevant module ...
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118 views

### How to numerically solve differential equations involving sines, cosines and inverses of the unknown function?

I'm very new to finite difference method and I am just introduced to methods of solving differential equation using finite difference method via sparse matrix method. I find that the main idea is to ...
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1 vote
212 views

### Solving 2D Poisson equation with mixed boundary conditions in Python

I am trying to numerically solve the Poisson's equation $$u_{xx} + u_{yy} = - \cos(x) \quad \text{if} - \pi/2 \leq x \leq \pi/2 \quad \text{0 otherwise}$$ The domain is the rectangle with vertices ...
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