Block Lanczos Tridiagonalization of
Complex Symmetric Matrices Matlab Package

Companion Papers     Download Package

1. Introduction

For any symmetric matrix A, there exists a special form of SVD, called Takagi factorization:

where Q is unitary and is the diagonal singular value matrix.

This package tridiagonalizes a complex symmetric matrix using block Lanczos algorithm. It is more efficient than the vector version. It can be followed by the divide-and-conquer method or the QR method for the symmetric SVD of a complex symmetric tridiagonal matrix to compute the Takagi factorization or symmetric SVD of a complex symmetric matrix.

2. Dependency

                            compare                            csgen
            ___________ _______|_______ ___________              |
           |           |               |           |         unitarand
         LanMPO    BlkLanCom        testinfo     errchk          |
                   BlkLanNorm                                  house
                       |
                    LanTri           
                       |        
                    sbmvmul                     
            

3. Functions

BlkLanCom.m Block Lanczos tridiagonalization of a complex-symmetric matrix using the componentwise orthogonalization.
BlkLanNorm.m Block Lanczos tridiagonalization of a complex-symmetric matrix using the normwise orthogonalization.
compare.m Compare the performance between componentwise and normwise orthogonalization scheme.
csgen.m Generate a random complex symmetric matrix with specified singular values.
errchk.m Check the errors of orthogonality and factorization of the block Lanczos algorithm.
house.m Householder transformation given a vector.
LanMPO.m Lanczos tridiagonalization of a complex-symmetric matrix using the modified partial orthogonalization.
LanTri.m Lanczos tridiagonalization of a complex-symmetric and block tridiagonal matrix.
sbmvmul.m Complex-symmetric and block tridiagonal matrix-vector multiplication.
testinfo.m Collect experiment results into a file.
unitarand.m Generate a random unitary matrix.
     

4. References

5. Download

6. Contact

Sanzheng Qiao
Professor, Department of Computing and Software
McMaster University, Hamilton, Ontario L8S 4K1, Canada
(905)-5259140 ext 27234

Developed by Guohong Liu. Last updated on May, 2005