A fixed-point implementation of matrix inversion using Cholesky decomposition

2006 ◽  
Author(s):  
A. Burian ◽  
J. Takala ◽  
M. Ylinen
Keyword(s):  
Fixed Point ◽  
Cholesky Decomposition ◽  
Matrix Inversion

scholarly journals On the Positive Definite Solutions of a Nonlinear Matrix Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1434-1438
Author(s):  
Ming Hui Wang ◽  
Chun Yan Liang ◽  
Shan Rui Hu
Keyword(s):  
Fixed Point ◽  
Matrix Equation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Positive Definite ◽  
Matrix Inversion ◽  
Nonlinear Matrix Equation ◽  
Nonlinear Matrix

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case are discussed. An algorithm that avoids matrix inversion with the case is proposed.

scholarly journals Improved Computing-Efficiency Least-Squares Algorithm with Application to All-Pass Filter Design

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Lo-Chyuan Su ◽  
Yue-Dar Jou ◽  
Fu-Kun Chen
Keyword(s):  
Least Squares ◽  
Filter Design ◽  
Linear Equations ◽  
Hankel Matrix ◽  
Cholesky Decomposition ◽  
Matrix Inversion ◽  
System Of Linear Equations ◽  
Computationally Efficient ◽  
Pass Filter ◽  
Simulation Results

All-pass filter design can be generally achieved by solving a system of linear equations. The associated matrices involved in the set of linear equations can be further formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided. Consequently, the optimal filter coefficients can be solved by using computationally efficient Levinson algorithms or Cholesky decomposition technique. In this paper, based on trigonometric identities and sampling the frequency band of interest uniformly, the authors proposed closed-form expressions to compute the elements of the Toeplitz-plus-Hankel matrix required in the least-squares design of IIR all-pass filters. Simulation results confirm that the proposed method achieves good performance as well as effectiveness.

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