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Code Listing by Andrew Knyazev

Code 1-10 of 10   






SUBSPACE(A,B) finds the largest angle between two subspaces specified by the columns of A and B. If A and B are vectors of unit length, this is the same as COS(ABS(A'*B)) in exact arithmetic. This is a replacement for MATLAB's SUBSPACE.m Rev. 5.5-5.8 that fails to provide correct answers for angles smaller than e-8 and for Rev. 5.9-5.10.4.3 that fails to provide correct answers for angles close to pi/2.



PCG Preconditioned Conjugate Gradients Method is a replacement of the standard built-in PCG code. Two new options are implemented: 'flex' and 'null'. The 'flex' option changes the standard PCG algorithm into the flexible one. It allows using...



MAJLE (Weak) Majorization check
S = MAJLE(X,Y) checks if the real part of X is (weakly) majorized by the real part of Y, where X and Y must be numeric (full or sparse) arrays. It returns S=0, if there is no weak majorization of X by Y, S=1,...



[blockVectorX,lambda]=lobpcg(blockVectorX,operatorA)
outputs the array of algebraic smallest eigenvalues lambda and
corresponding matrix of orthonormalized eigenvectors blockVectorX of the Hermitian (full or sparse) operator operatorA...



ORTHA Orthonormalization Relative to matrix A

Q=ortha(A,X)
Q=ortha('Afunc',X)

computes an orthonormal basis Q for the range of X, relative to the scalar product using a positive definite and selfadjoint matrix A. That...



The code computes the exact eigenpairs of (1-3)D negative Laplacian on a rectangular finite-difference grid for combinations of Dirichlet, Neumann, and Periodic boundary conditions using explicit formulas from



For a given real-valued function of one real variable on an interval, the code calculates the best approximation in the uniform (max) norm by a polynomial of a given degree. Approximating in a uniform norm is much computationally harder compared...



This demo shows examples of using the MATLAB Symbolic Math Toolbox for Ordinary Differential Equations (ODE). The examples range from relatively basic to rather advanced, and are placed according to the topics, as traditionally covered in...



Newton's method for solving a system of nonlinear equations, see http://en.wikipedia.org/wiki/Newton's_method

Newton(X,F,X0) solves nonlinear system F(x)=0 by Newton's method, using the given initial approximation X0. The derivative...



MATLAB sparse matrix converter to Hypre
MATLAB vector converter to Hypre
Hypre sparse matrix converter to MATLAB
Hypre vector converter to MATLAB

The Parallel High Performance Preconditioners (hypre) is a library of...