An example of solving nonlinear partial differential equation using mathematica - wolfram-mathematica

I was trying to solve a nonlinear partial differential equation using mathematica, but mathematica didn't provide a solution:
Did I make any mistake in the formation? or is it because the equation is too complicate?

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How solve equations about projection matrix

I'm read book about Computer Graphics with OpenGL (4th ed.) these formula come from Normalized Perspective-Projection
there are three equations:
and the book gives the parametric answer directly
there are four parameters:
I can only figure out S_z,I can't solve the equation for the other three parameters, who can give the detailed procedure of solving the equation

Convex Mixed-Integer for Non-Rigid Point Cloud Alignment

I am trying to approach non-rigid alignment using Convex Mixed-Integer Algorithm, but I am new to computer vision. Does anyone know some sample code that is similar - so that I can use that as a reference?
The algorithm is based on this research paper:
MINA: Convex Mixed-Integer Programming for Non-Rigid Shape Alignment
Thank you for showing interest in our work.
We model the constrained optimization problem in MATLAB with the help of YALMIP library and solve it using MOSEK.

Can 2D transpose convolution be represented as a Toeplitz matrix multiplication?

Can a 2D transpose convolution operation be represented as a matrix multiplication with the Toeplitz matrix, as can be done for a normal convolution?
I want to generalise some ideas from a dense network to a convolutional network. For normal convolutions, this is not a problem, as they can be represented as matrix multiplications with the Toeplitz matrix. But I couldn't find a clear mathematical formulation of transposed convolution, so I am not sure about this case.
I was looking for a mathematical answer, so should have probably asked somewhere else, anyways I think my latex write-up is correct and answers the question:
formula transposed convolution

Can we assign a new propagator different from domain and bounds in GECODE solver for solving linear constraints?

Linear equations/inequations can be easily solved by simplex algorithm which is very fast. But for GECODE solver we only have two propagators : domain and bounds which solve the constraints that have different approach for solving linear problems and have time complexity near to NP Hard. \n
Can we modify the GECODE solver code to assign a new propagator that will use the simplex algorithm for solving linear constraints? Any idea?

In triangulation, what are the geometric interpretations of midpoint algorithm, homogeneous linear least squares and nonlinear least squares method?

In "Multiple View Geometry in Computer Vision" Chapter 12. Structure Computation, page 310-313, triangulation is used for point 3D reconstruction. There are three methods mentioned:
Midpoint method that "finds the midpoint of the common perpendicular to the two rays in space".
Linear triangulation methods that uses SVD to solve homogeneous equation Ax = 0. In this method algebraic error is minimized.
Nonlinear triangulation method that uses iterative optimization algorithms e.g. LM to solve a nonlinear least square equation Ax = b. The "gold standard" reprojection error is minimized.
My question is:
What are the geometric interpretations of the three methods?
What are the differences between the three triangulation methods above?
I did some research and found some useful information:
This post explains that algebraic error assumes noise comes from 3D points, while reprojection error assumes noise comes from 2D image
These slides introduce three methods but did not provide explicit geometric interpretations.

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