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GEAR: A simple sparse matrix with known eigenvalues.

from the MMDELI

Matrix Generator GEAR
Source: C. W. Gear
Discipline: numerical linear algebra
Language: Java applet
Output format: Matrix Market format

This is a Java applet which generates an N-by-N matrix with ones on the sub- and super-diagonals, +1 or -1 in the (1,J) position, +1 or -1 in the (N,N+1-K) position, and zeros everywhere else.

All eigenvalues are of the form 2*COS(a) and the eigenvectors are of the form [SIN(w+a), SIN(w+2a), ..., SIN(w+Na)]. A can have double and triple eigenvalues and can be defective. The applet will compute the eigenvalues and eigenvectors on demand.

The diagonal is zero. The matrix is singular if J=K=N.

This generator was developed by Bruce Miller of NIST based on Nick Higham's Test Matrix Toolbox for MATLAB.


Norder of the matrix.
Joffset (from left) of extra nonzero in first row
A(1,J)+1 or -1
Koffset (from right) of extra nonzero in last row
A(N,N+1-K)+1 or -1


The Matrix Market is a service of the Mathematical and Computational Sciences Division / Information Technology Laboratory / National Institute of Standards and Technology.

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Last change in this page: Wed Sep 22 13:34:21 US/Eastern 2004 [Comments: ]