Journal Article10.1137/0215011
Computational complexity : on the geometry of polynomials and a theory of cost: II
Michael Shub,Steve Smale +1 more
TL;DR: Traditional algorithms, Newton's method and higher order generalization due to Euler are dealt with and some understanding of this phenomenon of finding a zero of a complex polynomial is given.
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Abstract: This paper deals with traditional algorithms, Newton’s method and a higher order generalization due to Euler. These iterations schemes and their modifications have had a great success in solving nonlinear systems of equations. We give some understanding of this phenomenon by giving estimates of efficiency. The problem we focus on is that of finding a zero of a complex polynomial.
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Citations
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Public-key cryptosystem based on invariants of diagonalizable groups
TL;DR: It is shown that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on the Euclidean algorithm).
1
C*-algebraic Smale Mean Value Conjecture and Dubinin-Sugawa Dual Mean Value Conjecture
K. Mahesh Krishna
- 16 Jun 2022
TL;DR: In this paper , the authors formulate the following conjectures for degree 2 C*-algebraic polynomials over commutative C *-algebras.
1
The Convergence Conditions of Interval Newton’s Method Based on Point Estimates
Zhe Li,Zhe Li,Baocheng Wan,Shugong Zhang +3 more
- 18 Sep 2017
TL;DR: By point estimates, this paper proposes the conditions under which the condition of Rump’s interval theorem holds and gives the convergence conditions of interval Newton's algorithm proposed by Rump.
•Posted Content
Smale's mean value conjecture for finite Blaschke products
Tuen-Wai Ng,Yongquan Zhang +1 more
TL;DR: In this article, the dual mean value conjecture for polynomials and its dual conjecture for finite Blaschke products was studied and a bound on the dual conjecture was obtained.
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TL;DR: In this article, the authors present a solution to the Matrix Eigenvalue Problem for linear systems of linear equations, based on linear algebra and linear algebra with nonlinear functions, which they call linear algebraic integration.
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Applied and Computational Complex Analysis
Henry C. Thacher,Peter Henrici +1 more
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