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By using a filter, those eigenpairs of a symmetric definite generalized eigenproblem "A v = lambda Bv" are solved whose eigenvalues are in a specified real interval "[a,b]". In present study, the filter we use is a polynomial of the real part of a linear combination of a few resolvents. Applications of a few resolvents are given by solving corresponding systems of linear equations. We are to solve these systems of linear equations by some matrix decomposition methods. Since we use a few resolvents, the number of matrix decompositions required is also a few (2 to 4).