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qtt_mg_interp

PURPOSE ^

The simplest multigrid operator in QTT as a TT-matrix

SYNOPSIS ^

function [m]=qtt_mg_interp(d)

DESCRIPTION ^

The simplest multigrid operator in QTT as a TT-matrix
   [M]=QTT_MG_INTERP(D) Computes the simplest MG-operator in the
   QTT-format on 2^D grid. Its stencil is
 1,    0
 0.5,    0.5
 0,    1
 0,    0.5


 TT-Toolbox 2.2, 2009-2012

This is TT Toolbox, written by Ivan Oseledets et al.
Institute of Numerical Mathematics, Moscow, Russia
webpage: http://spring.inm.ras.ru/osel

For all questions, bugs and suggestions please mail
ivan.oseledets@gmail.com
---------------------------

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [m]=qtt_mg_interp(d)
0002 %The simplest multigrid operator in QTT as a TT-matrix
0003 %   [M]=QTT_MG_INTERP(D) Computes the simplest MG-operator in the
0004 %   QTT-format on 2^D grid. Its stencil is
0005 % 1,    0
0006 % 0.5,    0.5
0007 % 0,    1
0008 % 0,    0.5
0009 %
0010 %
0011 % TT-Toolbox 2.2, 2009-2012
0012 %
0013 %This is TT Toolbox, written by Ivan Oseledets et al.
0014 %Institute of Numerical Mathematics, Moscow, Russia
0015 %webpage: http://spring.inm.ras.ru/osel
0016 %
0017 %For all questions, bugs and suggestions please mail
0018 %ivan.oseledets@gmail.com
0019 %---------------------------
0020 
0021 
0022 prol0 = [1 0; 0.5 0.5; 0 1; 0 0.5];
0023 h0 = [0 0; 0 0; 0 0; 0.5 0];
0024 I = eye(2);
0025 I12 = [0 1; 0 0];
0026 I21 = [0 0; 1 0];
0027 
0028 m = cell(d,1);
0029 
0030 m{1}=zeros(4,2,2);
0031 m{1}(:,:,1)=prol0; m{1}(:,:,2)=h0;
0032 for i=2:d-1
0033     m{i}=zeros(2,2,2,2);
0034     m{i}(:,:,1,1)=I;
0035     m{i}(:,:,2,1)=I12; m{i}(:,:,2,2)=I21;
0036 end; 
0037 m{d} = zeros(2,2,2);
0038 m{d}(:,:,1)=I; m{d}(:,:,2)=I12;
0039 
0040 m = tt_matrix(m);
0041 
0042 end

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