0
votes
0answers
17 views

How to measure the computational costs of solving CSPs and optimization problems?

I would like to define an abstract cost (machine and implementation independent measure) of the work needed to solve CSPs as a function of constraint and Jacobian evaluation counts. I am trying to ...
1
vote
0answers
36 views

Lanczos algorithm with thick restart on a dynamic matrix

According to a recommendation, this is a re-post of that. currently, I'm working on a way to compute the 2 biggest eigenvalues of a real, symmetric, huge and sparse matrix that changes a few entries ...
1
vote
1answer
33 views

oSVD and cSVD terms

In one article I faced with such terms as sSVD, cSVD and oSVD. As I understand sSVD - standart SVD, cSVD - svd for block-circulant matrices, but I can't find what is oSVD. 1) What is oSVD? 2) Can ...
1
vote
1answer
30 views

Is there a reference/source paper for the TUCKER_ALS() in Tensor Toolbox for MATLAB?

TUCKER_ALS computes the best rank-(R1,R2,..,Rn) approximation of tensor X, according to the specified dimensions. I am using MATLAB Tensor Toolbox Version 2.5. I am wondering if I write a paper, how ...
0
votes
0answers
31 views

Computational Science Masters programs [on hold]

I have been admitted to a few applied math, computational science, and scientific computing masters programs and am having trouble deciding where to attend. I was admitted to Georgia Tech, UPenn, NYU, ...
1
vote
0answers
36 views

Dense distributed matrix

A dense matrix is distributed for parallel computation column-wise, then multiplied from left & right by sparse matrices. What would be appropriate c++ libraries for these tasks?
0
votes
2answers
113 views

Interpolation by Solving a Minimization Problem (Optimization)

I will try to give the motivation behind this problem and later the math formality. Given a grayscale image (1 Channel - M by N Matrix). Someone marks some pixels as anchors. Now, you need to ...
0
votes
0answers
57 views

How to solve singular non symmetric poisson equation with Neumann boundary condtions?

I am trying to solve 2D Poisson equations with Neumann boundary conditions. When the mesh is uniform, Poisson equation is singular and symmetric, so the method listed in Null Space Projection for ...
1
vote
0answers
60 views

finite volume for diffusion equation with anisotropic (tensor) coefficient

Consider the scalar PDE for $u$ with Dirichlet boundary conditions: $\mathrm{div}(\mathcal{K}\nabla u) = f\; \forall x\; \in \Omega \subset R^2$, $u = 0 \; \forall \; x\;\in \partial\Omega$ ...
0
votes
1answer
32 views

Rank of image intensity matrix

I've been reading a paper about using Matrix Completion for Photometric Stereo but I am having some troubles in section 2.2 trying to understand why irrespective of the number of pixels and the number ...
0
votes
0answers
17 views

Bootstrap for a histogram

I create a set of $T$ trajectories with $P$ positions, $\{x_j\colon 0 \leq j < M\}$, with a Monte Carlo simulation. From this data, I calculate quantities like $\langle x \rangle$ and $\langle x^2 ...
0
votes
2answers
55 views

Data structure for a multiset that can be efficiently sampled from and updated

I'm writing a Monte Carlo simulation in which I have to maintain a large collection of not necessarily distinct items (i.e. a multiset, aka a bag). On each iteration I remove a random item from the ...
4
votes
2answers
109 views

Applying matrix square root inverse in matrix-free regime

Let $A$ be a large symmetric positive definite matrix, and suppose that we can efficiently apply $A$ and have a fast solver to apply $A^{-1}$, but we do not have access to the matrix entries for ...
0
votes
0answers
28 views

How to code on matlab for nonlinear systems?

How to code on matlab to solve arbitrary(not polynomial)nonlinear multivariable system of equations?like equations tagged under nonlinear systems of equation(see my equation I tagged)
0
votes
2answers
103 views

Systems of nonlinear equations

Consider the nonlinear system of equations $$ (1) \quad qk^2a_1^2E^2+wna_0a_1AE+pnka_0^2a_1E+rn^2a_0^2A^2-rn^2a_0^3A^2+qk^2a_0a_1ABE-qk^2na_0^2E^2=0, $$ $$ (2) \quad ...
0
votes
0answers
13 views

Keplerian Orbit Estimator

While calculating the eccentric anomaly of a satellite using the Newton-Raphson method, what initial estimate of the root for E (eccentric anomaly) should be taken for least number of iterations(best ...
0
votes
0answers
14 views

Finding eigenvalues of a Hermitian matrix using “eigsh” function from scipy

I am trying to use the scipy.linalg.sparse.eigsh function of scipy to find eigevalues of a Hermitian matrix. In the link below it says that eigsh can handle Hermitian matrices but when I run it gives ...
1
vote
1answer
75 views

Angular Velocity by Vector - 2D

This is originally a problem in programming, but since almost no one on Stackoverflow know how to solve this I went here instead; ...
0
votes
1answer
25 views

Angular Velocity by Vector - 2D [duplicate]

This is originally a problem in programming, but since almost no one on Stackoverflow know how to solve this I went here instead; ...
0
votes
2answers
56 views

WENO reconstruction of flux involving derivative terms

I have a set of modified compressible Euler equations that I would like to solve using a WENO method. The issue is that the modified flux function involves derivative and filtering terms and I'm not ...
1
vote
3answers
61 views

Fast way to compute integral of type $\int dx f(x) \cos(n \pi x)$ in SciPy

I have an integral of the form $$ I(n) = \int_0^1 dx f(x) \cos(n \pi x) , $$ where $n$ is an integer. In other words, I calculate the cosine Fourier coefficients of function $f$, which is real and ...
0
votes
0answers
14 views

Dimensioning in ANSYS design modeler

Say I have two parts with dimensions H50 and H51. I want to make H51 always equal to 1.5 H50 so that I only have to change H50, not H51 each time I run a new model. I tried to put H50 into the value ...
0
votes
0answers
14 views

Conceptual questions on Hopfield network and Particle Swarm

In continuation to http://stackoverflow.com/questions/22768493/neuralnetwork-activation-function/22918658?noredirect=1#22918658. I am using Hopfield network to recognize 3 characters = 0,1,2. I am ...
1
vote
2answers
120 views

Newton-Raphson method fails!

I am trying to solve an equation like $R(x) = 0$, using Newton-Raphson method. To obtain the $x$ increment in each iteration I solve $dx = -(A)^{-1}\cdot R$ where $A = dR/dx$. But the convergence ...
3
votes
2answers
123 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 ...
3
votes
3answers
145 views

How to solve a Linear Matrix Equation: AX-XA=B efficiently?

recently I have been working on solving some math problems using Fortran. There occurs to me that a linear matrix equation: $$ AX-XA=B $$ where $A$ and $B$ are known $n\times n$ matrices and $X$ is ...
0
votes
0answers
32 views

Snell's law & polarization in MATLAB

Does anyone have a script that simulates Snell's law involving polarization?
3
votes
1answer
97 views

Recommendations on FEM software for implementing Nitsche's method on interfaces between matching meshes?

Suppose: I have two domains, $\Omega_{1} = [0, 1/2] \times [0, 1]$ and $\Omega_{2} = [1/2, 1] \times [0, 1]$. The domains share an interface $\Gamma = \{1/2\} \times [0, 1] = \partial\Omega_{1} \cap ...
3
votes
3answers
70 views

Plane constraints in R3

I have multiple plane constraints in $\mathbb{R}^3$ of the form: $$n_i \cdot x \ge \delta_i$$ Where $n_i$ is the $i$th plane normal (in form (x, y, z)), $x$ is a point in space, and $\delta_i$ is ...
0
votes
1answer
44 views

Effect of Initial guess B (approximate Hessian) on BFGS algorithm

I am trying to implement BFGS. The purpose is to approximate Hessian matrix only (not using the quasi-newton optimization steps), so i am using steepest ascent for optimization. What I observe is that ...
3
votes
2answers
67 views

Fourier Transform of function in Spherical Harmonics

I have a function $f(r,\theta,\phi)$ which I am expressing in terms of spherical harmonics $$ f(r,\theta,\phi) = \sum_{l=0}^{\infty} \sum_{m=-l}^{l} g_{l,m}(r) d_{l,m}(\theta,\phi) $$ where ...
0
votes
0answers
15 views

SLATEC rouitne dslucs() and MKL correspondence

I am looking for a routine (or set of routines) in the Intel MKL that that can replace dslucs (Incomplete LU BiConjugate Gradient Squared Ax=b Solver) in ...
2
votes
1answer
63 views

Numerical spherical integration

In a high-dimensional setting, say $d \gg 5$, what is a recommended way of evaluating a spherical integral of a smooth (non-symmetric) function $f(\mathbf{x})$? $ \int_\mathcal{S_r} f(\mathbf{x}) ...
7
votes
2answers
222 views

What's the difference between conjugate gradient method and biconjugate gradient method

What's the difference between these two methods? Can a problem be solved by one method will be able to solved by the other? Can both/or one of them be parallelized with OpenMP and/or MPI?
1
vote
0answers
25 views

Interface Formulation at Finite Volume Boundaries when using the Dual Mesh

When using the dual mesh (vertex-centered) for finite volume methods, you end up with a cell center at the boundaries between materials. It is possible that the equations being solved in each ...
3
votes
1answer
57 views

The most efficient way to solve diffusion equation with concentrated initial condition

I want to solve the diffusion equation, i.e. $$ \dot{f} - f'' = 0 $$ with a boundary condition $f(0) = f(1) = 0$ and with an initial condition that $f$ is a boxcar function concentrated over some ...
0
votes
0answers
28 views

Given a 3x3 matrix, how to convert it into desired form with elementary row transforms?

Suppose matrix $A\in \mathbb{R}^{3\times 3}$ and rank($A$)=2; if $$A= \left( \begin{array}{c} a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\\ \end{array} ...
6
votes
3answers
98 views

How to determine the amount of FLOPs my computer is capable of

I would like to determine the theoretical number of FLOPs (Floating Point Operations) that my computer can do. Can someone please help me with this. (I would like to compare my computer to some ...
2
votes
1answer
57 views

SVD and HITS Algorithm Power Iterations

As we know, computing the authority (or hub) score of HITS ranking method, means to use the following matrix equation: $$ \textbf{a}^{k}=A^T A\textbf{a}^{(k-1)} $$ and apply the power iteration ...
1
vote
1answer
69 views

System of nonlinear equations in MATLAB

I've got some problems solving (numerically) this system of equations. \begin{array}{l} 40 \cdot \cos (2t) + 105 \cdot \cos ({\theta _3}) - 75 \cdot \cos ({\theta _4}) - 91.924 \cdot \cos ({337.62}) ...
3
votes
2answers
96 views

2nd order centered finite-difference approximation of $u_{xy}$

The problem is to find a 2nd order finite difference approximation of the partial derivative uxy, where u is a function of x and y. Page 5 of this pdf I found does a centered difference approximation ...
2
votes
1answer
53 views

Finding Interior eigenvalues using Davidson algorithm

Is it possible to find interior eigenvalues closer to some lambda using Davidson method. I was searching online but found that most people use Jacobi-Davidson method for that. Thanks
2
votes
1answer
130 views

Good Finite Element Library for a small project

I'm currently working on this project and I have a basic structural analyzer that uses the finite element method. Essentially, I turn each block into a set of trusses, construct a stiffness matrix ...
0
votes
1answer
50 views

How to model waterflow when only a couple of sample points available

Figure below depicts a cross section of a creek for which I am trying to measure the water flow for that section. What we have as inputs are a bunch of sample points on the river. For each sample ...
0
votes
1answer
34 views

computing the inverse of a large block diagonal sparse matrix in r

I would like to compute the inverse of some large block diagonal sparse matrix. The number of rows and columns is somewhat over 50,000. The blocks are 12 by 12 and are sparse (27 non zero elements). ...
3
votes
1answer
40 views

Finding the minimum hamming distance between a bit vector and any pairwise intersection of multiple bit vectors

I'm looking for a way to optimize this procedure. This is the problem: I have a list of bit vectors $\mathbf{A} = [ a_1, a_2, a_3, ..., a_n ]$ I have a list of bit vectors $\mathbf{B} = [ b_1, b_2, ...
1
vote
0answers
36 views

data structures for efficient/easy implementation of finite volume method for 2D Poisson equation

My question is about implementation alone. Consider a square domain with regular square, cell centred finite volumes. This is for the multiscale finite volume method (Jenny and Lunati) I need to ...
1
vote
0answers
54 views

Assembling sparse matrix in PETSC for Poisson equation

I am a novice at PETSC, and I have been trying to write an FVM code for steady heat conduction in 2D using PETSC (square, regular grid, Dirichlet boundaries) Since the large matrix , say A, will be ...
5
votes
1answer
60 views

Computing eigendecomposition of a Hermitian matrix that is almost unitary

I have a dense Hermitian matrix that is approximately unitary, so it has eigenvalues that are $\sim \pm1$. I would like to compute all the eigenvectors corresponding to the $+1$ eigenvalue (not ...
1
vote
2answers
69 views

Do vendors release their own LAPACK library?

Every CPU vendor seems to make BLAS libraries that are specialized to run on their hardware. Do they do the same for LAPACK? Or is that a non-issue because LAPACK is written entirely in terms of BLAS ...

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