| Summary: | To solve a system of equations that needs few updates, such as sparse systems, the leading dichotomous coordinate descent (DCD) algorithm is better than the cyclic DCD algorithm because of its fast speed of convergence. In the case of sparse systems requiring a large number of updates, the cyclic DCD algorithm converges faster and has a lower error level than the leading DCD algorithm. However, the leading DCD algorithm has a faster convergence speed in the initial updates. In this paper, we propose a combination of leading and cyclic DCD iterations, the leading-cyclic DCD algorithm, to improve the convergence speed of the cyclic DCD algorithm. The proposed algorithm involves two steps. First, by properly selecting the number of updates of the solution vector used in the leading DCD algorithm, a solution is obtained from the leading DCD algorithm. Second, taking the output of the leading DCD algorithm as the initial values, an improved soft output is generated by the cyclic DCD algorithm with a large number of iterations. Numerical results demonstrate that when the solution sparsity <inline-formula> <math display="inline"> <semantics> <mi>γ</mi> </semantics> </math> </inline-formula> is in the interval <inline-formula> <math display="inline"> <semantics> <mrow> <mo>[</mo> <mn>1</mn> <mo>/</mo> <mn>8</mn> <mo>,</mo> <mn>6</mn> <mo>/</mo> <mn>8</mn> <mo>]</mo> </mrow> </semantics> </math> </inline-formula>, the proposed leading-cyclic DCD algorithm outperforms both the existing cyclic and leading DCD algorithms for all iterations.
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