کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4599515 | 1631143 | 2014 | 19 صفحه PDF | دانلود رایگان |
Decay patterns of matrix inverses have recently attracted considerable interest, due to their relevance in numerical analysis, and in applications requiring matrix function approximations. In this paper we analyze the decay pattern of the inverse of banded matrices of the form S=M⊗In+In⊗MS=M⊗In+In⊗M where M is tridiagonal, symmetric and positive definite, InIn is the identity matrix, and ⊗ stands for the Kronecker product. It is well known that the inverses of banded matrices exhibit an exponential decay pattern away from the main diagonal. However, the entries in S−1S−1 show a non-monotonic decay, which is not caught by classical bounds. By using an alternative expression for S−1S−1, we derive computable upper bounds that closely capture the actual behavior of its entries. We also show that similar estimates can be obtained when M has a larger bandwidth, or when the sum of Kronecker products involves two different matrices. Numerical experiments illustrating the new bounds are also reported.
Journal: Linear Algebra and its Applications - Volume 452, 1 July 2014, Pages 21–39