In this paper, the author proved a relational expression between shift a and rotary angle 0 in implicit shifted QL process for a symmetric irreducible tridiagonal matrix and designed a new method, in which some information would be made up for those 'graded' matrices whose shift may be drowned during performing implicit QL process so that defects of both implicit and explicit ones are avoided. The numerical examples in the last section show that this new scheme is always efficient and valuable.
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