Spectral bounds for \(\| A^{-1}\| _{\infty}\)
The author studies the spectral bounds for \(\| A^{- 1}\|_{\infty}\), where A is a positive definite Hermitian matrix. In the main theorem of the paper it is proved that if \(A^ m\) has no more than km non-zero entries in each row then we obtain \(\| A^{- 1}\|_{\infty}\leq 33\sqrt{k}\| A\|_ 2^{1/4}\| A^{- 1}\|_ 2^{5/4}.\) The author conjectures that the index 5/4 could be lowered to 1, perhaps with associated changes in the remaining quantities. In another proposition it is shown that if A belongs to a certain subclass of bi-infinite Hermitian Toeplitz matrices then \(\| A^{-1}\|_ 2=\| A^{-1}\|_{\infty}\).
scientific article; zbMATH DE number 4002725