Pitfalls and Guidelines for the Numerical Evaluation of Moderate-order System Frequency ResponseNASA, 1981 - 36 pages |
From inside the book
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Page 5
... power series " form , that is : P1 ( x ) = ( • • n n • ( ( A ̧ x + A ̧ . ̧ ) x + A ̧ . 2 ) x + • n - 2 · · + A1 ) x + A。( 4 ) = Σ A , xi = 0 For frequency response analysis , this is not the end ( see Wilkinson , Reference 35 , page 47 ) ...
... power series " form , that is : P1 ( x ) = ( • • n n • ( ( A ̧ x + A ̧ . ̧ ) x + A ̧ . 2 ) x + • n - 2 · · + A1 ) x + A。( 4 ) = Σ A , xi = 0 For frequency response analysis , this is not the end ( see Wilkinson , Reference 35 , page 47 ) ...
Page 18
... power series form . This , for moderate- to large - order systems , is an ill - conditioned computing problem ... power series form . These are normally obtained via a sequence of algebraic operations with functions of polynomials . As ...
... power series form . This , for moderate- to large - order systems , is an ill - conditioned computing problem ... power series form . These are normally obtained via a sequence of algebraic operations with functions of polynomials . As ...
Page 20
... series of determinantal equa- tions , in which matrix elements are low - order polynomials in power series form . It should be noted that , at this point , polynomial coefficients can still be considered as " primary data . " Let the ...
... series of determinantal equa- tions , in which matrix elements are low - order polynomials in power series form . It should be noted that , at this point , polynomial coefficients can still be considered as " primary data . " Let the ...
Contents
POLYNOMIAL AND RATIONAL FORMS FOR TRANSFER | 4 |
SYSTEM EQUATIONS PRIMARY DATA | 16 |
REDUCED ORDER SYSTEM EQUATIONS | 23 |
Common terms and phrases
accuracy associated with equation B₂ block diagram C₁ C₂ companion matrix complex plane computed results COMPUTED)/EXACT D₁ damped digits double precision eigenanalysis eigensystem EISPACK exact solution factored polynomial form follow-on frequency domain ill-conditioned computing problem ill-conditioned problems initial data input instinctive methods large order large-order systems low order low-degree polynomials MATRIX ELEMENTS matrix exponential matrix inversion matrix of polynomials method of Leverrier method Reference moderate to large moderate-order systems NASA Neumann and Goldstine Non-Oscillatory System numerator polynomial numerical error analysis numerical methods obtaining transfer functions order state variable oscillatory systems partial fraction expansion Pitfalls and Guidelines polynomials in power POLYRT COMPUTED ROOTS poorly-conditioned power series form present results associated primary data quasi-upper triangular QZ-algorithm QZ-method rational functions Reference 14 root-finding algorithm round-off error simulation models stable algorithm subroutine summarize a large system definition data System Frequency Response system order increases Table theory tions transfer function matrix well-conditioned system