SparseJSR：基于稀疏SOS分解的联合谱半径快速算法
SparseJSR: A Fast Algorithm to Compute Joint Spectral Radius via Sparse SOS Decompositions
摘要：
研究了稀疏矩阵情况下联合谱半径的计算问题。我们提供了一个稀疏的变种的Parrilo和Jadbabaie提出的程序，计算上界的JSR的平方和（SOS）松弛。我们得到的迭代算法，称为SparseJSR，是基于长期稀疏SOS（TSSOS）框架，由王，Magron和Lasserre开发，产生SOS分解的多项式与任意稀疏支持。SparseJSR利用输入矩阵的稀疏性来显著减少与JSR计算相关的计算负担。我们的算法框架，然后成功地应用于计算JSR的上界，随机生成的基准，以及所产生的问题的控制器的稳定性证明，在可能的硬件和软件故障。
英文摘要：
This paper focuses on the computation of joint spectral radii (JSR), when the involved matrices are sparse. We provide a sparse variant of the procedure proposed by Parrilo and Jadbabaie, to compute upper bounds of the JSR by means of sum-of-squares (SOS) relaxations. Our resulting iterative algorithm, called SparseJSR, is based on the term sparsity SOS (TSSOS) framework, developed by Wang, Magron and Lasserre, yielding SOS decompositions of polynomials with arbitrary sparse support. SparseJSR exploits the sparsity of the input matrices to significantly reduce the computational burden associated with the JSR computation. Our algorithmic framework is then successfully applied to compute upper bounds for JSR, on randomly generated benchmarks as well as on problems arising from stability proofs of controllers, in relation with possible hardware and software faults.
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