In his study of Newton s root approximation method Smale de ned the Newto nian graph of a complex univariate polynomial f The vertices of this graph are the roots of f and f and the edges are the degenerate curves of ow of the Newtonian vector eld Nf z f z f z The embedded edges of this graph form the boundaries of root basins in Newton s root approximationmethod The graph de nes a treelike rel...

Many of the “counterintuitive” features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I.E. Segal and, more recently, G. Fleming (in a paper entitled “Reeh-Schlieder meets Newton-Wigner”) have propo...

Many of the “counterintuitive” features of relativistic quantum field theory have their formal root in the Reeh-Schlieder theorem, which in particular entails that local operations applied to the vacuum state can produce any state of the entire field. It is of great interest then that I.E. Segal and, more recently, G. Fleming (in a paper entitled “Reeh-Schlieder meets Newton-Wigner”) have propo...

Three algorithm implementations for square root computation are considered in this paper. Newton-Raphson's, iterative, and binary search algorithm implementations are completely designed, verified and compared. The algorithms, entire system-on-chip realisations and their functioning are described.

We introduce a new iterative root-finding method for complex polynomials, dubbed Newton-Ellipsoid method. It is inspired by the Ellipsoid method, a classical method in optimization, and a property of Newton’s Method derived in [7], according to which at each complex number a half-space can be found containing a root. Newton-Ellipsoid method combines this property, bounds on zeros, together with...

In this paper, we present a three-step multilingual dependency parser based on a deterministic shift-reduce parsing algorithm. Different from last year, we separate the root-parsing strategy as sequential labeling task and try to link the neighbor word dependences via a near neighbor parsing. The outputs of the root and neighbor parsers were encoded as features for the shift-reduce parser. In a...

The discretization of Gross-Pitaevskii equations (GPE) leads to a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv). We use two Newton-based methods compute the positive ground state GPE. first method comes from Newton-Noda iteration for saturable Schrödinger proposed by Ching-Sung Liu, which can be transferred GPE naturally. second combines idea root-finding and Newton method, ...