Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Dynamics of Feedback Systems
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Efficient Applications of Invariants to Harmonic Balance Equation Using Gröbner Base
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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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 Gröbner 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.