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N-port matrix conversions
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Mathematical background
Subsections
N-port matrix conversions
Renormalization of S-parameters to different port impedances
Transformations of n-Port matrices
Two-Port transformations
Two-Port matrix conversion based on current and voltage
Two-Port matrix conversion based on signal waves
Mixed Two-Port matrix conversions
Two-Port parameters of passive devices
Solving linear equation systems
Matrix inversion
Gaussian elimination
Step 1: Forward elimination
Finding an appropriate pivot element
Step 2: Backward substitution
Gauss-Jordan method
LU decomposition
Step 1: LU decomposition
Step 2: Forward substitution
Step 3: Backward substitution
QR decomposition
Step 1: QR decomposition
Step 2: Forming the new right hand side
Step 3: Backward substitution
Motivation
QR decomposition with column pivoting
Least norm problem
Singular value decomposition
Notation
Householder reflector
Specific case
General case
Givens rotation
Eigenvalues of a 2-by-2 matrix
Step 1: Bidiagonalization
Step 2: Matrix reconstructions
Step 3: Diagonalization - shifted QR iteration
Single shifted QR step.
Computation of the Wilkinson shift.
Zeros on the diagonal or super-diagonal.
Step 4: Solving the equation system
Jacobi method
Gauss-Seidel method
A comparison
Polynomial approximations
Cubic splines
Frequency-Time Domain Transformation
Fast Fourier Transformation
Real-Valued FFT
More-Dimensional FFT
This document was generated by
Stefan Jahn
on
2007-12-30
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