Rank: 643 based on 112 downloads (last 30 days) and 11 files submitted
photo

Andrew Knyazev

E-mail
Company/University
University of Colorado Denver

Personal Profile:

http://math.ucdenver.edu/~aknyazev/

Professional Interests:
matrix computations, numerical PDEs, data mining

 

Watch this Author's files

 

Files Posted by Andrew View all
  • 1 - 5 of
  • 11
Updated   File Tags Downloads
(last 30 days) 		Comments Rating
06 Jan 2012 Screenshot Newton's method done right Newton's method for solving systems of nonlinear equations, including nonsquare and inconsistent Author: Andrew Knyazev demo, newton, modeling, matrix, physics, nonlinear 17 2
08 Dec 2011 Screenshot ODE Tutorial Demo Advanced examples of using the MATLAB Symbolic Math Toolbox for Ordinary Differential Equations Author: Andrew Knyazev ode, symbolic, movies, demo, physics, mathematics 4 0
17 Oct 2011 Screenshot lobpcg.m LOBPCG solves Hermitian partial generalized eigenproblems using preconditioning, competes with eigs Author: Andrew Knyazev linear algebra, symmetric, partial, eigenproblems, preconditioning, eigenproblem 13 6
  • 4.5
4.5 | 2 ratings
14 Sep 2011 Screenshot Best polynomial approximation in uniform norm For a given function on an interval, the code calculates the min-max approximation by a polynomial. Author: Andrew Knyazev mathematics, statistics, optimization, approximation, polynomial, minimax 5 0
03 Sep 2011 Screenshot pcg.m with 'null' and 'flex' options Preconditioned Conjugate Gradients handles homogeneous equations and nonsymmetric preconditioning Author: Andrew Knyazev linear algebra, preconditioned, conjugate, gradients, mathematics, matrix 7 0
Comments and Ratings by Andrew View all
  • 1 - 5 of
  • 15
Updated File Comments Rating
22 Oct 2012 Newton's method done right Newton's method for solving systems of nonlinear equations, including nonsquare and inconsistent Author: Andrew Knyazev

The code works in Symbolic Math Toolbox 5.7 (R2011b). Previous versions of the toolbox may not support creating symbolic vectors this way. There may be other issues, too, with prior unsupported versions of the toolbox.

12 Mar 2012 Laplacian in 1D, 2D, or 3D Sparse (1-3)D Laplacian on a rectangular grid with exact eigenpairs. Author: Andrew Knyazev

Re: Marios Karaoulis

It depends on boundary conditions. Your example apparently uses Neumann boundary condition as is http://en.wikipedia.org/wiki/Laplacian_matrix#As_an_approximation_to_the_negative_continuous_Laplacian
while the code default us the Dirichlet boundary conditions. To get your matrix, please use

[~,~,A]=laplacian([3 3],{'NN' 'NN'})

full(A) shows what you want:

2 -1 0 -1 0 0 0 0 0
-1 3 -1 0 -1 0 0 0 0
0 -1 2 0 0 -1 0 0 0
-1 0 0 3 -1 0 -1 0 0
0 -1 0 -1 4 -1 0 -1 0
0 0 -1 0 -1 3 0 0 -1
0 0 0 -1 0 0 2 -1 0
0 0 0 0 -1 0 -1 3 -1
0 0 0 0 0 -1 0 -1 2

12 Oct 2011 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup

Simple, general and nice! The best I have on the block so far.

Missing: limit number of steps, check for stagnation. default for the tolerance.

Cannot you just always use F_prime_X\F_X ?

12 Oct 2011 Numerical Analysis Functions 1 Functions for the Bisection, Fixed-Point, Newton-Raphson, and Muller's methods. Author: Jonathan Lister

Well written.

12 Oct 2011 Newton's Method Finds better successive approximations for the root of a function using Newton's Method. Author: Harmon Amakobe

"Number of iterations will be increased accordingly in order to meet the set tolerance value" - in other words the "ite" parameter is always ignored. The code never stops if the tolerance is not met.

Comments and Ratings on Andrew's Files View all
  • 1 - 5 of
  • 21
Updated File Comment by Comments Rating
22 Oct 2012 Newton's method done right Newton's method for solving systems of nonlinear equations, including nonsquare and inconsistent Author: Andrew Knyazev Knyazev, Andrew

The code works in Symbolic Math Toolbox 5.7 (R2011b). Previous versions of the toolbox may not support creating symbolic vectors this way. There may be other issues, too, with prior unsupported versions of the toolbox.

22 Oct 2012 Newton's method done right Newton's method for solving systems of nonlinear equations, including nonsquare and inconsistent Author: Andrew Knyazev Xu

Hey,man! X=sym('X',[2 1]); is not a valid command..... Tried your algorithm, but did not work.
14 Mar 2012 Laplacian in 1D, 2D, or 3D Sparse (1-3)D Laplacian on a rectangular grid with exact eigenpairs. Author: Andrew Knyazev Karaoulis, Marios

Thanks for the reply Andrew, you are right.

12 Mar 2012 Laplacian in 1D, 2D, or 3D Sparse (1-3)D Laplacian on a rectangular grid with exact eigenpairs. Author: Andrew Knyazev Knyazev, Andrew

Re: Marios Karaoulis

It depends on boundary conditions. Your example apparently uses Neumann boundary condition as is http://en.wikipedia.org/wiki/Laplacian_matrix#As_an_approximation_to_the_negative_continuous_Laplacian
while the code default us the Dirichlet boundary conditions. To get your matrix, please use

[~,~,A]=laplacian([3 3],{'NN' 'NN'})

full(A) shows what you want:

2 -1 0 -1 0 0 0 0 0
-1 3 -1 0 -1 0 0 0 0
0 -1 2 0 0 -1 0 0 0
-1 0 0 3 -1 0 -1 0 0
0 -1 0 -1 4 -1 0 -1 0
0 0 -1 0 -1 3 0 0 -1
0 0 0 -1 0 0 2 -1 0
0 0 0 0 -1 0 -1 3 -1
0 0 0 0 0 -1 0 -1 2

11 Mar 2012 Laplacian in 1D, 2D, or 3D Sparse (1-3)D Laplacian on a rectangular grid with exact eigenpairs. Author: Andrew Knyazev Karaoulis, Marios

Hi, useful add on, but one question.
Let's say we have a 3x3 grid, then why all the element on the diagonal are 4? Should be something like this
[2 -1 0 -1 0 0 0 0 0
-1 3 -1 0 -1 0 0 0
0 -1 2 0 0 -1 0 0 0 ....

...]

Only line 5 should have 4 on it's diagonal.
Top Tags Applied by Andrew
  • 1 - 5 of
  • 58
mathematics, linear algebra, matrix, statistics, angle
Files Tagged by Andrew View all
  • 1 - 5 of
  • 11
Updated   File Tags Downloads
(last 30 days) 		Comments Rating
06 Jan 2012 Screenshot Newton's method done right Newton's method for solving systems of nonlinear equations, including nonsquare and inconsistent Author: Andrew Knyazev demo, newton, modeling, matrix, physics, nonlinear 17 2
08 Dec 2011 Screenshot ODE Tutorial Demo Advanced examples of using the MATLAB Symbolic Math Toolbox for Ordinary Differential Equations Author: Andrew Knyazev ode, symbolic, movies, demo, physics, mathematics 4 0
17 Oct 2011 Screenshot lobpcg.m LOBPCG solves Hermitian partial generalized eigenproblems using preconditioning, competes with eigs Author: Andrew Knyazev linear algebra, symmetric, partial, eigenproblems, preconditioning, eigenproblem 13 6
  • 4.5
4.5 | 2 ratings
14 Sep 2011 Screenshot Best polynomial approximation in uniform norm For a given function on an interval, the code calculates the min-max approximation by a polynomial. Author: Andrew Knyazev mathematics, statistics, optimization, approximation, polynomial, minimax 5 0
03 Sep 2011 Screenshot pcg.m with 'null' and 'flex' options Preconditioned Conjugate Gradients handles homogeneous equations and nonsymmetric preconditioning Author: Andrew Knyazev linear algebra, preconditioned, conjugate, gradients, mathematics, matrix 7 0

Contact us