Efficient and accurate algorithms for computing matrix trigonometric functions

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• 作者：Pedro Alonso^a ; ^{palonso@dsic.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Javier Ibá ; ñ ; ez^b ; ^{jjibanez@dsic.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Jorge Sastre^c ; ^{jorsasma@iteam.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Jesú ; s Peinado^b ; ^{jpeinado@dsic.upv.es" class="auth_mail" title="E-mail the corresponding author} ; Emilio Defez^d ; ^{edefez@imm.upv.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Matrix cosine ; Matrix sine ; Scaling and squaring method ; Taylor series ; Backward error ; Parallel implementation
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：325-332
• 全文大小：475 K

文摘

Trigonometric matrix functions play a fundamental role in second order differential equations. This work presents an algorithm based on Taylor series for computing the matrix cosine. It uses a backward error analysis with improved bounds. Numerical experiments show that MATLAB implementations of this algorithm has higher accuracy than other MATLAB implementations of the state of the art in the majority of tests. Furthermore, we have implemented the designed algorithm in language C for general purpose processors, and in CUDA for one and two NVIDIA GPUs. We obtained a very good performance from these implementations thanks to the high computational power of these hardware accelerators and our effort driven to avoid as much communications as possible. All the implemented programs are accessible through the MATLAB environment.