# Questions tagged [projection]

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### 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 ...
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 ...
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 ...
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 \...
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 ...
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 ...
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: $\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$ ...
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) ...
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 ...
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 ...
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 ...
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 ...
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 $P(x)$. ...
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 ...
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 ...
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 ...