Volume 16, Issue 2
A Note on Generic Fiedler Matrices
DOI:

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 140-146

Published online: 2007-05

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• Abstract

In this paper, we first show that a generic $m \times n$ Fiedler matrix may have $2^{m - n - 1} - 1$ kinds of factorizations which are very complicated when $m$ is much larger than $n$. In this work, two special cases are examined, one is an $m \times n$ Fiedler matrix being factored as a product of $( {m - n})$ Fiedler matrices, the other is an $m \times ( {m - 2} )$ Fiedler matrix's factorization. Then we discuss the relation among the numbers of parameters of three generic $m \times n$, $n \times p$ and $m \times p$ Fiedler matrices, and obtain some useful results.

• Keywords

@Article{NM-16-140, author = { L. Q. Zhao}, title = {A Note on Generic Fiedler Matrices}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {2}, pages = {140--146}, abstract = { In this paper, we first show that a generic $m \times n$ Fiedler matrix may have $2^{m - n - 1} - 1$ kinds of factorizations which are very complicated when $m$ is much larger than $n$. In this work, two special cases are examined, one is an $m \times n$ Fiedler matrix being factored as a product of $( {m - n})$ Fiedler matrices, the other is an $m \times ( {m - 2} )$ Fiedler matrix's factorization. Then we discuss the relation among the numbers of parameters of three generic $m \times n$, $n \times p$ and $m \times p$ Fiedler matrices, and obtain some useful results.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8052.html} }
TY - JOUR T1 - A Note on Generic Fiedler Matrices AU - L. Q. Zhao JO - Numerical Mathematics, a Journal of Chinese Universities VL - 2 SP - 140 EP - 146 PY - 2007 DA - 2007/05 SN - 16 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/nm/8052.html KW - AB - In this paper, we first show that a generic $m \times n$ Fiedler matrix may have $2^{m - n - 1} - 1$ kinds of factorizations which are very complicated when $m$ is much larger than $n$. In this work, two special cases are examined, one is an $m \times n$ Fiedler matrix being factored as a product of $( {m - n})$ Fiedler matrices, the other is an $m \times ( {m - 2} )$ Fiedler matrix's factorization. Then we discuss the relation among the numbers of parameters of three generic $m \times n$, $n \times p$ and $m \times p$ Fiedler matrices, and obtain some useful results.