Results 261 to 270 of about 9,265,494 (295)
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The Mathematical Intelligencer, 1987
The paper presents a short but very essential review of the main ideas on the homotopy continuation method of solving polynomial systems by means of reducing them to some Cauchy problem for a corresponding system of ordinary differential equations. Starting from a simple example the author discusses all the possible difficulties in the application of ...
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The paper presents a short but very essential review of the main ideas on the homotopy continuation method of solving polynomial systems by means of reducing them to some Cauchy problem for a corresponding system of ordinary differential equations. Starting from a simple example the author discusses all the possible difficulties in the application of ...
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On Series of Orthogonal Polynomials and Systems of Classical Type Polynomials
Ukrainian Mathematical Journal, 2021If \(\sum_{k=0}^{\infty} c_{k} g_{k}(x)\) is a formal series of orthonormal polynomials \(g_{k}(x)\) on the real line with positive coefficients \(c_{k}\), then its partial sums \(u_{n}(x)\) are associated with Jacobi-type pencils. Therefore, they possess a recurrence relation and special orthonormality conditions.
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A Hybrid Polynomial System Solving Method for Mixed Trigonometric Polynomial Systems
SIAM Journal on Numerical Analysis, 2008Mixed trigonometric polynomial systems arise in many fields of science and engineering. Commonly, this class of systems is transformed into polynomial systems by variable substituting and adding some quadratic equations, and then solved by some polynomial system solving method.
Bo Yu 0003, Bo Dong 0011
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Equalization of recursive polynomial systems
IEEE Signal Processing Letters, 1999This letter presents some theorems for the exact and pth-order equalization of nonlinear systems described by recursive polynomial input-output relationships. It is shown that the nonlinear equalizers derived on the basis of this theory have simple and computationally efficient structures.
Alberto Carini +2 more
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Controllability of structured polynomial systems
IEEE Transactions on Automatic Control, 1999Summary: Two algorithms, based on the Gröbner basis method, which facilitate the controllability analysis for a class of polynomial systems are presented. We combine these algorithms with some recent results on output dead-beat controllability in order to obtain sufficient, as well as necessary, conditions for complete and state dead-beat ...
Dragan Nesic, Iven M. Y. Mareels
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THE NUMBER OF ROOTS OF A POLYNOMIAL SYSTEM
Bulletin of the Australian Mathematical Society, 2020AbstractLet I be a zero-dimensional ideal in the polynomial ring $K[x_1,\ldots ,x_n]$ over a field K. We give a bound for the number of roots of I in $K^n$ counted with combinatorial multiplicity. As a consequence, we give a proof of Alon’s combinatorial Nullstellensatz.
NGUYEN CONG MINH +2 more
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PM, a system for polynomial manipulation
Communications of the ACM, 1966PM is an IBM 7094 program system for formal manipulation of polynomials in any number of variables, with integral coefficients unrestricted in size. Some of the formal opeartions which can be performed by the system are sums, differences, products, quotients, derivatives, substitutions and greatest common divisors.
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Singular systems of polynomials
Proceedings of the 1998 international symposium on Symbolic and algebraic computation, 1998Hans J. Stetter, Günther H. Thallinger
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On Polynomial Systems in a Banach Ring
Journal of Mathematical Physics, 1965We define and discuss equations on Banach rings (algebras) which are of polynomial form. We prove a local uniqueness theorem for the homogeneous case, and an existence and local uniqueness theorem for the nonhomogeneous case. In order to apply these results to the equations of Lagrangian quantum field theory we find it necessary to extend the concept ...
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Nonlinear Systems: A Polynomial Approach
2009The modern development of nonlinear control theory is related mainly to the use of algebraic methods which show great applicability to solve a number of nonlinear control problems. Recently, the power of such methods were extended by introducing the concept of transfer functions of nonlinear systems.
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