# 稀疏矩阵

 稀疏矩陣的例子 ${\displaystyle \left[{\begin{smallmatrix}11&22&0&0&0&0&0\\0&33&44&0&0&0&0\\0&0&55&66&77&0&0\\0&0&0&0&0&88&0\\0&0&0&0&0&0&99\\\end{smallmatrix}}\right]}$ 上述稀疏矩陣僅包含9個非零元素，另外包含26個零元素。其稀疏度為74%，密度為26%。

## 定义

${\displaystyle b_{n}(\mathbf {A} ):=\mathrm {min} _{1\leq m\leq M}\lbrace m\mid a_{n,m}\neq 0\rbrace }$

${\displaystyle B(\mathbf {A} ):=\mathrm {max} _{1\leq n\leq N}b_{n}(\mathbf {A} )}$

## 參考文獻

• Golub, Gene H.; Van Loan, Charles F. Matrix Computations 3rd. Baltimore: Johns Hopkins. 1996. ISBN 978-0-8018-5414-9.
• Stoer, Josef; Bulirsch, Roland. Introduction to Numerical Analysis 3rd. Berlin, New York: Springer-Verlag. 2002. ISBN 978-0-387-95452-3.
• Tewarson, Reginald P. Sparse Matrices (Part of the Mathematics in Science & Engineering series). Academic Press Inc. May 1973. (This book, by a professor at the State University of New York at Stony Book, was the first book exclusively dedicated to Sparse Matrices. Graduate courses using this as a textbook were offered at that University in the early 1980s).
• Bank, Randolph E.; Douglas, Craig C. Sparse Matrix Multiplication Package (PDF). [2019-02-09]. （原始内容 (PDF)存档于2014-12-21）.
• Pissanetzky, Sergio. Sparse Matrix Technology. Academic Press. 1984.
• Snay, Richard A. Reducing the profile of sparse symmetric matrices. Bulletin Géodésique. 1976, 50 (4): 341. doi:10.1007/BF02521587. Also NOAA Technical Memorandum NOS NGS-4, National Geodetic Survey, Rockville, MD.