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### How to solve nonlinear optimization with constraints that have singular jacobian

I'm solving a nonlinear constrained optimization with constraint of following form: $$\mathbf{A}^T\mathbf{A}-\mathbf{I}=\mathbf{0}, \mathbf{B}^T\mathbf{B}-\mathbf{I}=\mathbf{0}$$ where $\mathbf{A}$ ...
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### Problem with cell size and boundary conditions in transient cylindrical conduction

I am attempting to model the steady state behavior of a cylinder using the finite volume method (FVM) subjected to a variety of boundary conditions in Matlab. First off, I am treating the cylinder as ...
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### Size reduction of matrices in dispersion curve calculation

I have an energy dispersion curve obtained from the eigenvalues of $$E(k) = \text{eig}(T e^{ik} + T^H e^{-ik} + H_0),$$ where $H_0$ and $T$ are $N\times N$ square matrices, $T^H$ is the Hermitian ...
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### How to solve advection equation using semi-lagrangian method?

I am working on something that involves solving an advection equation $\partial{x}/\partial{t}+\vec{u}\cdot\nabla{x}=0$ in 3D. I discretized the space into 3d cartesian grid and used the Semi-...
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### Determine set of dividend and divisor for quotient

I have the following Problem: I know the range within the results of a division must lie. [ quotientrange ] Additionally, the quotient should not exceed a certain number of fractions. I know, that ...
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Consider a node $s$. Let's assume that there are three outgoing arcs from node $s$ namely $(s,i)$,$(s,j)$ and $(s,k)$. Corresponding to each of these arcs, there is a flow proportion value $t_{sj}\in (... 0answers 100 views ### Anisotropic cover with n-cuboids I'm working on an algorithm for which I would like to cover an$n$-dimensional unit cube by a set of$n$-cuboids (i.e.,$n$-dimensional rectangles). The size and orientation of these cuboids is ... 0answers 81 views ### Constraint solving over modular domains I have a set of constraints over modular domains e.g.$\exists a \in A_i : x \equiv a \pmod{n_i}$for all$i=0,\ldots,k$The question is, does such an$x$exist? I've been pointed to method of ... 0answers 58 views ### Assembled human ESTs for annotation I am annotating protein-coding genes in a region of the human genome and am looking for a set of assembled ESTs I can use as evidence for constructing gene models. A quick search of NCBI's SRA shows 4,... 1answer 175 views ### GPU libraries for integer matmul | overflow tolerated Are there any high performance integer BLAS libraries that implement matrix multiplication i.e. i32gemm and i64gemm ? I need to use them for a cryptographic application and can tolerate overflows, i.e.... 1answer 794 views ### lapack singular matrix I'd like to find a condition that allows me to determine if a matrix is invertible or not. naively, I computed the determinant to see if it was zero. but then I realized that even for very small ... 1answer 339 views ### Eigenvalue problem with periodic boundary conditions: Are my eigenvalues correct? I am using a (central) finite difference scheme to solve the eigenvalue problem $$-\frac{d^2}{dx^2}u = \lambda u$$ with periodic boundary conditions on a unit interval. I use arpack's zndrv1 and ... 0answers 63 views ### How to debug segmentation faults in large problems? I am sorry if this question seems like off topic or opinion based, but I was not sure how to go about it. I am currently working on a 100k x 100k positive definite linear system and trying to solve it ... 0answers 49 views ### 4th Order Adams-Moulton Method C++ I am trying to solve an ODE using 4th Order Runge Kutta and the 4th Order Adams-Moulton Method. I iterate over a couple of thousand timesteps and it seems to hold fine when the values are constant(... 0answers 49 views ### FEM Meshing artifact at nodes with fewer neighbors I wrote a 2D-FEM solver to solve some diffusion process and wanted to verify my code with a test problem. The input was$f(x,y) = x^2+y^2$and I applied the stiffness matrix on it to get$\Delta f = 4$... 0answers 29 views ### Numerical simulation for a bounded process. Is slight deviation a “normal” fact? Suppose I have to numerically simulate a process$\{y_t\}$such that$y_t\geq0\forall t\in\mathbb{N}$, with$t$denoting time-step. Let's suppose I use MonteCarlo with$\mathscr{N}$simulation ... 0answers 19 views ### Scale of x-axis for Fourier transform Consider a function$f(t)$and its Fourier transform$F(\omega)$. The amplitude of the Fourier transform$F(\omega)$depends on the frequency$\omega$and thus also depends on the scale of the$t\$-...

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