Eigenvalues of Tridiagonal Matrices in MATLAB

Description

• TRIDEIG computes all the eigenvalues of a symmetric tridiagonal matrix.
  
• BIDSVD computes all the singular values of a bidiagonal matrix.
• MAXEIG computes the largest eigenvalue of a symmetric tridiagonal matrix.

The functions are implemented as MEX-file wrappers to the LAPACK functions DSTEQR, DBDSQR, and DSTEBZ.

Download

• trideig.m - Help file
• trideig.c - Source
• trideig.mexw32 - Windows 32-bit binary
• trideig.mexw64 - Windows 64-bit binary
• trideig.mexa64 - Linux 64-bit binary

• bidsvd.m - Help file
• bidsvd.c - Source
• bidsvd.mexw32 - Windows 32-bit binary
• bidsvd.mexw64 - Windows 64-bit binary
• bidsvd.mexa64 - Linux 64-bit binary

• maxeig.m - Help file
• maxeig.c - Source
• maxeig.mexw32 - Windows 32-bit binary
• maxeig.mexw64 - Windows 64-bit binary
• maxeig.mexa64 - Linux 64-bit binary

• all.zip - Everything (ZIP file)

The binaries are compiled on MATLAB R2010b.

Example

Compute and plot the eigenvalues of the 1000-by-1000 matrix

>> n=1000;
>> l=trideig(2*ones(n,1),-ones(n-1,1));
>> plot(l)

Compare with the exact expression

>> l0=2-2*cos(pi*(1:n)'/(n+1));
>> norm(l-l0,inf)

ans =

6.6613e-015