Complex Symmetric Matrices Matlab Package

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.

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

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.

- Sanzheng Qiao, Guohong Liu, and Wei Xu. in Advanced Signal Processing Algorithms, Architectures, and Implementations XV, edited by Franklin T. Luk, Proc. of SPIE Vol. 5910, 591010 (2005). (ps, pdf)

- Download whole package: package.zip
- Download source code of functions:
BlkLanCom.m BlkLanNorm.m compare.m csgen.m errchk.m house.m LanMPO.m LanTri.m sbmvmul.m testinfo.m unitarand.m

Professor, Department of Computing and Software

McMaster University, Hamilton, Ontario L8S 4K1, Canada

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