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This paper proposes a new software architecture framework, named FIBER, to generalize auto-tuning facilities and obtain highly accurate estimated parameters. The FIBER framework also provides a loop unrolling function, needing code generation and parameter registration processes, to support code development by library developers. FIBER has three kinds of parameter optimization layers–installation, before execution-invocation, and run-time. An eigensolver parameter to apply the FIBER framework is described and evaluated in three kinds of parallel computers; the HITACHI SR8000/MPP, Fujitsu VPP800/63, and Pentium4 PC cluster. Evaluation indicated a 28.7% speed increase in the computation kernel of the eigensolver with application of the new optimization layer of before execution-invocation.