Computer algebra: symbolic and algebraic computation (2nd ed.)
Computer algebra: systems and algorithms for algebraic computation
Computer algebra: systems and algorithms for algebraic computation
Algorithms for polynomial real root isolation
Algorithms for polynomial real root isolation
An Exact Method for Finding the Roots of a Complex Polynomial
ACM Transactions on Mathematical Software (TOMS)
A modified Newton method for polynomials
Communications of the ACM
Polynomial real root isolation by differentiation
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
The philosophy of nothing and everything
APL '95 Proceedings of the international conference on Applied programming languages
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An exact and practical method for determining the number, location, and multiplicity of all real zeros of the trigonometric polynomials is described. All computations can be performed without loss of accuracy. lThe method is based on zero isolation techniques for algebraic polynomials. An efficient method for the calculation of the coefficients of a corresponding algebraic polynomial is stated. The complexity of trigonometric zero isolation depending on the degree and the coefficient size of the given trigonometric polynomial is analyzed. In an experimental evaluation, the performance of the method is compared to the performance of recently developed numeric techniques for the approximate determination of all roots of trigonometric polynomials. The case of exponential or hyperbolic polynomials is treated in an appendix.