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Harmonic balance (HB) method is well known principle for analyzing periodic oscillations on nonlinear networks and systems. Because the HB method has a truncation error, approximated solutions have been guaranteed by error bounds. However, its numerical computation is very time-consuming compared with solving the HB equation. This paper proposes an algebraic representation of the error bound using Grobner base. The algebraic representation enables to decrease the computational cost of the error bound considerably. Moreover, using singular points of the algebraic representation, we can obtain accurate break points of the error bound by collisions.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.9 pp.2442-2449

- Publication Date
- 2008/09/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1093/ietfec/e91-a.9.2442

- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

- Category
- Analysis, Modelng and Simulation

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Masakazu YAGI, Takashi HISAKADO, Kohshi OKUMURA, "An Algebraic Approach to Guarantee Harmonic Balance Method Using Grobner Base" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 9, pp. 2442-2449, September 2008, doi: 10.1093/ietfec/e91-a.9.2442.

Abstract: Harmonic balance (HB) method is well known principle for analyzing periodic oscillations on nonlinear networks and systems. Because the HB method has a truncation error, approximated solutions have been guaranteed by error bounds. However, its numerical computation is very time-consuming compared with solving the HB equation. This paper proposes an algebraic representation of the error bound using Grobner base. The algebraic representation enables to decrease the computational cost of the error bound considerably. Moreover, using singular points of the algebraic representation, we can obtain accurate break points of the error bound by collisions.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.9.2442/_p

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@ARTICLE{e91-a_9_2442,

author={Masakazu YAGI, Takashi HISAKADO, Kohshi OKUMURA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={An Algebraic Approach to Guarantee Harmonic Balance Method Using Grobner Base},

year={2008},

volume={E91-A},

number={9},

pages={2442-2449},

abstract={Harmonic balance (HB) method is well known principle for analyzing periodic oscillations on nonlinear networks and systems. Because the HB method has a truncation error, approximated solutions have been guaranteed by error bounds. However, its numerical computation is very time-consuming compared with solving the HB equation. This paper proposes an algebraic representation of the error bound using Grobner base. The algebraic representation enables to decrease the computational cost of the error bound considerably. Moreover, using singular points of the algebraic representation, we can obtain accurate break points of the error bound by collisions.},

keywords={},

doi={10.1093/ietfec/e91-a.9.2442},

ISSN={1745-1337},

month={September},}

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TY - JOUR

TI - An Algebraic Approach to Guarantee Harmonic Balance Method Using Grobner Base

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2442

EP - 2449

AU - Masakazu YAGI

AU - Takashi HISAKADO

AU - Kohshi OKUMURA

PY - 2008

DO - 10.1093/ietfec/e91-a.9.2442

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E91-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2008

AB - Harmonic balance (HB) method is well known principle for analyzing periodic oscillations on nonlinear networks and systems. Because the HB method has a truncation error, approximated solutions have been guaranteed by error bounds. However, its numerical computation is very time-consuming compared with solving the HB equation. This paper proposes an algebraic representation of the error bound using Grobner base. The algebraic representation enables to decrease the computational cost of the error bound considerably. Moreover, using singular points of the algebraic representation, we can obtain accurate break points of the error bound by collisions.

ER -