Conjugate Gradients as Direct Method

Zdeněk Dostál ()
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Zdeněk Dostál: VŠB - Technical University Ostrava, National Super computer Center and Department of Applied Mathematics

Chapter 4 in Optimal Quadratic Programming and QCQP Algorithms with Case Studies, 2025, pp 99-106 from Springer

Abstract: Abstract 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 .

Date: 2025
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DOI: 10.1007/978-3-031-95167-1_4

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