论文标题
相关矩阵序列的多级对称toeplitz结构和光谱分布结果
Multilevel symmetrized Toeplitz structures and spectral distribution results for the related matrix-sequences
论文作者
论文摘要
近年来，研究了由计算目的的动机，已经研究了由Lebesgue综合函数产生的Toeplitz矩阵对称性的奇异值和光谱特征。 Indeed, under the assumptions that $f$ belongs to $L^1([-π,π])$ and it has real Fourier coefficients, the spectral and singular value distribution of the matrix-sequence $\{Y_nT_n[f]\}_n$ has been identified, where $n$ is the matrix-size, $Y_n$ is the anti-identity matrix, and $T_n[f]$是由$ f $生成的toeplitz矩阵。在本注中，我们考虑由$ f \在l^1中产生的多级toeplitz矩阵$ t _ {\ bf n} [f] $（[ - π，π]^k）$，$ \ bf n $是多index，是一个多数index，是一个多index，nide y size size size sige seque prove spectral和matrix y $ $ $ $ \ y \ y \ \ \ ar y \ ar y \。 n} t _ {\ bf n} [f] \} _ {\ bf n} $带有$ y _ {\ bf n} $是反认同矩阵的相应张力。
In recent years, motivated by computational purposes, the singular value and spectral features of the symmetrization of Toeplitz matrices generated by a Lebesgue integrable function have been studied. Indeed, under the assumptions that $f$ belongs to $L^1([-π,π])$ and it has real Fourier coefficients, the spectral and singular value distribution of the matrix-sequence $\{Y_nT_n[f]\}_n$ has been identified, where $n$ is the matrix-size, $Y_n$ is the anti-identity matrix, and $T_n[f]$ is the Toeplitz matrix generated by $f$. In this note, we consider the multilevel Toeplitz matrix $T_{\bf n}[f]$ generated by $f\in L^1([-π,π]^k)$, $\bf n$ being a multi-index identifying the matrix-size, and we prove spectral and singular value distribution results for the matrix-sequence $\{Y_{\bf n}T_{\bf n}[f]\}_{\bf n}$ with $Y_{\bf n}$ being the corresponding tensorization of the anti-identity matrix.
