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Matrices, Continued Fractions, and Some Early History of Iteration Theory

Continued fractions of the form \( \frac{1}{1 + \frac{c}{1 + \frac{c}{ 1 +\ddots}}}  \) are analyzed using linear algebra and iteration theory.  The continued fractions of interest are closely related to a class of \(2 \times 2\) matrices, and the eigenvalues and eigenvectors of those matrices are investigated to determine when the corresponding continued fractions converge.  Historical references are included.

Old Node ID: 
3401
MSC Codes: 
97H60
Author(s): 
Michael Sormani (College of Staten Island CUNY)
Publication Date: 
Monday, February 8, 2010
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
April, 2000
Subject(s): 
Algebra and Number Theory
Linear Algebra
Topic(s): 
Linear Algebra
Eigenvalues and Eigenvectors
History of Linear Algebra
Matrix Algebra
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Publish Page: 
Furnished by JSTOR: 
Rating Count: 
22.00
Rating Sum: 
65.00
Rating Average: 
2.95
Applicable Course(s): 
3.8 Linear/Matrix Algebra
Modify Date: 
Monday, February 8, 2010
Average: 3 (22 votes)

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