# Questions tagged [linear-system]

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The PDE I am working with: $$\partial_tu = \nabla \cdot (a(x)\nabla u)-\beta(x)u\\ \partial_nu=0, x \in \Omega \subset \mathbb{R}^2\\ \beta(x)>0$$ Integrate the PDE: $$\int_\Omega \partial_t u=\... 1answer 425 views ### Least-squares for a diagonal matrix This is a follow-up to a different question I asked with more detail. For v\in\mathbb{R}^n, denote D_v\in\mathbb{R}^n as the diagonal matrix with elements in v. Given a "tall" matrix B\in\... 2answers 246 views ### Solving “Hadamard systems” Suppose we have two matrices A and B (we can assume they're symmetric; if absolutely necessary I think they may be positive definite). Then, is there any technique for solving$$(A\circ B)x=b,$$... 3answers 2k views ### What is the best solver for solving a large sparse indefinite system What's the best solver that can solve a large sparse but indefinite matrix? 2answers 347 views ### How “sparse” should a sparse matrix be to see benefits? I have a matrix, whose size scales as 2^N (assume even N). In each row of the matrix, only about 2^{N/2} of the entries are filled (N can be somewhere between 10 and 40, depending on what's ... 1answer 799 views ### How to implement flexible gmres in matlab? About the flexible GMRES (fgmres), we know that it is a variant of right preconditioned gmres. And the robust command gmres in matlab as follows: ... 3answers 352 views ### PRIMA gives an unstable result? I am working with Modified Nodal Admittance representation of circuits. I am doing Model Order Reduction using PRIMA on MATLAB. I am considering these circuits as Descriptor State-Space systems. I ... 2answers 193 views ### 1D FEM for nonlinear diffusion coefficient I want to solve with linear finite elements the equation$$\partial_t u = \partial_{x}(a(u)\partial_xu)$$in the domain t \in [0,1] and x \in [-L,L]. Here a(u) is just a function of u. ... 5answers 1k views ### Speed of solving linear system with block diagonal matrix I have a bunch of 3x3 linear systems of the form Ax=b. In general, would it be faster to solve each individual system, or to formulate it as a giant block diagonal system and solve that? I expect ... 2answers 329 views ### Solve a very large linear system (question about a library linear algebra to do this) I need to solve a very large linear system (coming from finite element method). I'm currently using the Intel MKL library, but the system has been delayed more than 20 hours. The matrix of the system ... 0answers 60 views ### Kronecker-factored least-squares? Suppose a_i,b_i are d\times 1 matrices, y_i is scalar, and I need to find least-squares solution w of the following system of n equations:$$y_i=(a_i^T\otimes b_i^T)w Is there a ...
I am studying the reverse mode of automatic differentiation. The reverse mode of automatic differentiation allows the efficient computation of a the derivative of a single dependent variable $y$ with ...