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