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First, we show how to use a conjugate basis to reduce the minimization of a quadratic function to solve the class of scalar QP problems. Then, we introduce the conjugate gradient method as a tool for constructing a conjugate basis using minimizers of the cost function in expanding Krylov spaces and related gradients to generate a conjugate basis and to find the solution in a finite number of steps. We postpone the analysis of intermediate iterations to Chap. 8 .

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Conjugate Gradients as Direct Method

  • 章节

  • 发表日期：

    2025年

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  • Zdeněk Dostál

摘要

First, we show how to use a conjugate basis to reduce the minimization of a quadratic function to solve the class of scalar QP problems. Then, we introduce the conjugate gradient method as a tool for constructing a conjugate basis using minimizers of the cost function in expanding Krylov spaces and related gradients to generate a conjugate basis and to find the solution in a finite number of steps. We postpone the analysis of intermediate iterations to Chap. 8 .