High-speed high-accuracy matrix singular value decomposition method, program, and device

A singular value decomposition method according to the present invention is a method for performing a singular value decomposition on an arbitrary matrix A using a computer, the method including the steps of: performing an upper bidiagonalization on the matrix A so as to obtain an upper bidiagonal matrix B of the matrix A; obtaining at least one singular value of the matrix B as singular values of the matrix A; and obtaining a singular vector of the matrix A for the . The step of obtaining a singular vector of the matrix A includes a step of performing a Twisted decomposition on a matrix BTB− 2I (where I is a unit matrix) by using a Miura inverse transformation, an sdLVvs transformation, an rdLVvs transformation and a Miura transformation so as to diagonalize a matrix BTB.