Numerical Instability of Resultant Methods for Multidimensional Rootfinding
نویسندگان
چکیده
منابع مشابه
Numerical Instability of Resultant Methods for Multidimensional Rootfinding
Hidden-variable resultant methods are a class of algorithms for solving multidimensional polynomial rootfinding problems. In two dimensions, when significant care is taken, they are competitive practical rootfinders. However, in higher dimensions they are known to miss zeros, calculate roots to low precision, and introduce spurious solutions. We show that the hidden variable resultant method ba...
متن کاملAre resultant methods numerically unstable for multidimensional rootfinding?
Hidden-variable resultant methods are a class of algorithms for solving multidimensional polynomial rootfinding problems. In two dimensions, when significant care is taken, they are competitive practical rootfinders. However, in higher dimensions they are known to miss zeros, calculate roots to low precision, and introduce spurious solutions. We show that the hidden-variable resultant method ba...
متن کاملNumerical methods for multidimensional radiative transfer∗
This paper presents a continuous finite element method for solving the resonance line transfer problem in moving media. The algorithm is capable of dealing with three spatial dimensions, using hierarchically structured grids which are locally refined by means of duality-based a-posteriori error estimates. Application of the method to coherent isotropic scattering and complete redistribution giv...
متن کاملNUMERICAL ANALYSIS MEETS NUMBER THEORY: USING ROOTFINDING METHODS TO CALCULATE INVERSES MOD p
In this article we explore a very interesting application of tools from numerical analysis to number theory. As the title suggests, we will see how one can use classical rootfinding methods, such as Newton’s method, to calculate the reciprocal of an integer modulo p, where p is a prime number. We first encountered this idea in [3], where Newton’s method was used to find the reciprocal of a fini...
متن کاملSufficient Conditions for the Instability of Numerical Integration Methods * Abbas
(March 5, 1969) In a previous paper, a general theorem was investigated for the s tability of numerical integration methods for the so lution of systems of diffe rentia l equation s. In thi s paper, further theore ms are developed as suffi c ie nt conditions for the instability of nume rica l integration methods. Applying these theore ms , the ins:abiljt.y of known formula s are checked eas ily...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2016
ISSN: 0036-1429,1095-7170
DOI: 10.1137/15m1022513