scholarly journals Solving matrix polynomial equations with nested continued fractions

2021 ◽  
pp. 57-61
Author(s):  
Mykola Nedashkovskyy
Keyword(s):  
Continued Fractions ◽  
Arbitrary Order ◽  
Matrix Polynomial ◽  
Polynomial Equations

A new general approach for solving matrix polynomial equations of arbitrary order with matrix or vector unknowns is proposed in the work with the use of nested continued fractions.

Matrix Polynomial Equations in Control Theory 1

1978 ◽  
Vol 11 (1) ◽  
pp. 1135-1140
Author(s):  
R. Rutman ◽  
Y. Shamash
Keyword(s):  
Control Theory ◽  
Matrix Polynomial ◽  
Polynomial Equations

scholarly journals ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS

2017 ◽  
Vol 13 (2) ◽  
pp. 7147-7154
Author(s):  
Anthony G Shannon ◽  
Charles K Cook b ◽  
Rebecca A. Hillman c
Keyword(s):  
Continued Fractions ◽  
Arbitrary Order ◽  
Fibonacci Numbers ◽  
Recursive Sequences ◽  
Essential Idea ◽  
Associated Continued Fractions ◽  
Generalized Continued Fractions

The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to generalized continued fractions with matrices as the unifying elements.

scholarly journals About the solvability of matrix polynomial equations

2017 ◽  
Vol 49 (4) ◽  
pp. 670-675 ◽  
Author(s):  
Tim Netzer ◽  
Andreas Thom
Keyword(s):  
Matrix Polynomial ◽  
Polynomial Equations
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