TY - JOUR

T1 - Optimal fraction-free routh tests for complex and real integer polynomials

AU - Bistritz, Yuval

PY - 2013

Y1 - 2013

N2 - The Routh test is the simplest and most efficient algorithm to determine whether all the zeros of a polynomial have negative real parts. However, the test involves divisions that may decrease its numerical accuracy and are a drawback in its use for various generalized applications. The paper presents fraction-free forms for this classical test that enhance it with the property that the testing of a polynomial with Gaussian or real integer coefficients can be completed over the respective ring of integers. Two types of algorithms are considered one, named the G-sequence, which is most efficient (as an integer algorithm) for Gaussian integers, and another, named the R-sequence, which is most efficient for real integers. The G-sequence can be used also for the real case, but the R-sequence is by far more efficient for real integer polynomials. The count of zeros with positive real parts for normal polynomials is also presented for each algorithm.

AB - The Routh test is the simplest and most efficient algorithm to determine whether all the zeros of a polynomial have negative real parts. However, the test involves divisions that may decrease its numerical accuracy and are a drawback in its use for various generalized applications. The paper presents fraction-free forms for this classical test that enhance it with the property that the testing of a polynomial with Gaussian or real integer coefficients can be completed over the respective ring of integers. Two types of algorithms are considered one, named the G-sequence, which is most efficient (as an integer algorithm) for Gaussian integers, and another, named the R-sequence, which is most efficient for real integers. The G-sequence can be used also for the real case, but the R-sequence is by far more efficient for real integer polynomials. The count of zeros with positive real parts for normal polynomials is also presented for each algorithm.

KW - Continuous-time systems

KW - Routh-Hurwitz criterion

KW - integer algorithms

KW - linear network analysis

KW - polynomials

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=84883390383&partnerID=8YFLogxK

U2 - 10.1109/TCSI.2013.2246232

DO - 10.1109/TCSI.2013.2246232

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84883390383

SN - 1549-8328

VL - 60

SP - 2453

EP - 2464

JO - IEEE Transactions on Circuits and Systems I: Regular Papers

JF - IEEE Transactions on Circuits and Systems I: Regular Papers

IS - 9

M1 - 6507577

ER -