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Subgroup Parameters based on Orthogonal Factorization

A new methodology to produce subgroup parameters has been developed based on orthogonal factorization of weighting functions. In the existent methods the weighting functions do not appear explicitly, which causes the inconvenience in producing subgroup parameters in some situations. In the present method, the weighting functions are tailored to the required conditions by the use of orthonormal factorization method of which mathematical background is based on the Lanczos method. The obtained weighting functions can be commonly used for any physical quantities in order to produce corresponding subgroup parameters. The superiority of this approach becomes eminent especially when multiple conditions are specified at the same time. The numerical results of two simple examples have revealed the potential of the applicability of the present method to general problems. We have concluded that the present method may be developed into an efficient tool to deal with wide variety of problems using subgroup-method-related methodology.