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- W2016794976 abstract "Let $F = [f_{ij}]$, $1 < i$, $j leqq q$, be a measurable, nonnegative definite $q times q$ matrix-valued function defined on the unit circle $C$. It is known that when $mathbfit {F}$ and $log det textbf {F}$ are in $L_1(C)$, $mathbfit {F}$ admits a factorization of the form $F = mathbf {Phi } mathbf {Phi }^ast$, where $mathbf {Phi }$ is an optimal, full rank function in $L_2^{0+}(C)$. Under the additional assumption that ${ (prod nolimits _{i = 1}^q f_{ii})/det F}$ is in $L_1(C)$, an iterative procedure which yields an infinite series for $mathbf {Phi }$ in terms of $mathbfit {F}$ is given. The optimal function $mathbf {Phi }$ plays a significant role in the multivariate prediction theory of stochastic processes. The present work generalizes the results of several authors concerning the determination of the optimal factor $mathbf {Phi }$." @default.
- W2016794976 created "2016-06-24" @default.
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- W2016794976 date "1971-02-01" @default.
- W2016794976 modified "2023-09-26" @default.
- W2016794976 title "On determination of the optimal factor of a nonnegative matrix-valued function" @default.
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- W2016794976 doi "https://doi.org/10.1090/s0002-9939-1971-0278056-0" @default.
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