Questions tagged [projection]

The tag has no usage guidance.

18 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
5
votes
0answers
67 views

Padua-type pointset for functions singular on line $x=y$

The Padua points $\mathrm{Pad}_{n} \subset [-1,1]^{2}$ are a unisolvent pointset with optimal growth of Lebesgue constant, described in detail here. With some work they can be used to generate a ...
5
votes
0answers
696 views

Generating pseudo-random orthonormal bases for random projection

I am performing series of random projections i.e. projecting the input matrix onto randomly generated orthonormal bases (of much lower dimensionality). The projection is just a matrix multiplication ...
3
votes
0answers
114 views

Backward stable algorithm to get orthogonal projection onto the column space of a matrix

I have to find the orthogonal projection of a vector $b$ onto the matrix $A$ of size $m \times n$. In my application, I don't have the luxury of calculating the QR factorization. All I have are ...
2
votes
1answer
113 views

Project to nearest point on convex polyhedron

I have a point $y \in \mathbb{R}^d$ and a convex polyhedron $\mathcal{P}$ given as the intersection of half-spaces: $$\mathcal{P} = \{x \in \mathbb{R}^d \mid a_1 \cdot x \le b_1, \dots, a_n \cdot x \...
2
votes
0answers
58 views

Geometric interpretation of lemma

I am currently studying eigenvalue problems. I already worked through the Minimax-principles, seen why $\lambda_{h, m} \geq \lambda_m$, when comparing the eigenvalues of a discretization and the ...
2
votes
0answers
154 views

How to obtain the reduced model from a subspace projection method?

I have a system of ordinary differential equations (ODEs). It is a large system that has dozens of equations and hundreds of parameters. I wish to reduce its size so it becomes computationally more ...
2
votes
0answers
290 views

Treatment of Neumann (Traction) boundary conditions using projection methods

I am looking to solve the incompressible Navier-Stokes equations in 3D, using an inflow boundary condition specifying a velocity: $\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$ ...
1
vote
0answers
83 views

Matlab - Equality between 2 Fisher matrices constructed in a different way

I want to know if, on a Fisher matrix, the projection operation (with a Jacobian matrix) commutes with a matricial inversion operation. The 2 ways to build these 2 matrices are: 1) First method: 1.1) ...
1
vote
0answers
54 views

Why does including the pressure in this FVM for Stokes 2nd Problem lead to wrong solutions?

I'm trying to learn how to use finite volume methods and I want to solve a more general case of Stokes' second problem i.e. an infinite half-plane oscillating harmonically with no-slip boundary ...
1
vote
0answers
92 views

Lumped mass matrices for higher-order finite elements for CFD

Given that some of the mass lumping techniques, for example, row-sum lumping does not produce practically viable lumped mass matrices for all the element shapes, what are the techniques used for mass ...
1
vote
0answers
95 views

Stokes problem with imposed acceleration on boundaries (projection scheme)

I am trying to solve FSI problems with finite elements and using a projection scheme (I am taking as reference the review of Guermond: Guermond, J. L.; Minev, P.; Shen, Jie, An overview of ...
1
vote
0answers
74 views

Stable Method of orthogonal projection onto a subspace with the help of Moore-Penrose inverse,

Projection of a vector $v$ onto the column space of a matrix $A$ is given by $AA^\dagger v$. From the definition of Moore-Penrose Inverse we know that $AA^\dagger v = (A^T)^\dagger A^T v $. Below is ...
1
vote
0answers
86 views

How does this Constrained Minimization algorithm work?

I don't fully understand the subsection 3.2 Constrained minimization of this paper. In particular, I don't understand the first step "Register active set" and the definition of projection $P(x)$. ...
1
vote
0answers
292 views

How to obtain projections from sinogram in ART reconstruction technique?

I'm kind new in the Computed Tomography field and I'm trying to understand and implement ART technique. Said it, I started to read the book The Mathematics of Medical Imaging - A Beginners Guide by ...
1
vote
0answers
87 views

Oscillations in Chorin's method due to the BC

I am pretty new to the CFD and I wanted to start with Chorin's projection. The starting problem is just a free jet flowing in the investigated area. I got terrible oscillations almost immediately and ...
1
vote
0answers
36 views

BC's for intermediate velocities in Implicit Fractional Step Methods

Lately, I was reading some seminal papers on Fractional Step Algorithms and I found this one: Kim, D., Choi, H. A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on ...
1
vote
0answers
61 views

Mass-conservative reprojection (on a sphere)

I have a 2D distribution of mass on a sphere given as a matrix of masses in latitude-longitude grid cells. I need these masses projected to another grid on the same sphere with different location of ...
0
votes
0answers
134 views

Do the projection (with Jacobian) and marginalisation (inversion of matrix and remove a row/column and reinversion) commute?

I try to check the equality or the inequality between 2 Fisher matrices. The goal is too see if the projection (with Jacobian) and marginalisation (inversion of matrix and remove a row/column and ...