Several efficient methods for derivative-free optimization (DFO) are based on the construction and maintenance of an interpolation model for the objective function. Most of these algorithms use special “geometry-improving” iterations, where the geometry (poisedness) of the underlying interpolation set is made better at the cost of one or more function evaluations. We show that such geometry imp...

The de Broglie-Bohm formulation of the Schrodinger equation implies conservation of the wave function probability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate a...

The interpolated free group factors L(Fr) for 1 < r ≤ ∞, (also defined by F. Rădulescu) are given another (but equivalent) definition as well as proofs of their properties with respect to compression by projections and free products. In order to prove the addition formula for free products, algebraic techniques are developed which allow us to show R∗R ∼= L(F2) where R is the hyperfinite II1–fac...

5 The Proof of Theorem 2.1. 27 5.1 Estimates for Tl,m, l ≥ 0, m < −l. . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.2 Estimates for Tl,m, l ≥ 0, m > 0. . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.3 Estimates for Tl,m, l ≥ 0, −l ≤ m ≤ 0. . . . . . . . . . . . . . . . . . . . . . . . 33 5.4 Estimates for T (ε) l R −1 i0 , l ≥ 0. . . . . . . . . . . . . . . . . . . . . . . . ...

In this paper we classify all ideal projections from C[x, y] onto the linear span of 1, x, y. In particular we show that every such projection is a limit of interpolating projections. That verifies one particular case of a conjecture of C. deBoor. §

We introduce a new structured kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce kernel approximations for fast computations through kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpo...

We study the communication complexity of combinatorial auctions via interpolation mechanisms that interpolate between non-truthful and truthful protocols. Specifically, an interpolation mechanism has two phases. In the first phase, the bidders participate in some non-truthful protocol whose output is itself a truthful protocol. In the second phase, the bidders participate in the truthful protoc...

Computationally intensive applications such as sound synthesis, animation, scientific computation, can take advantage of table-lookup interpolation to reduce computation and execution time. When designing table-lookup interpolation, application writers face various choices such as table size and interpolation mechanism (linear, quadratic, etc). The better the interpolation, the more intensive t...

Fuzzy inference systems provide a simple yet effective solution to complex non-linear problems, which have been applied to numerous real-world applications with great success. However, conventional fuzzy inference systems may suffer from either too sparse, too complex or imbalanced rule bases, given that the data may be unevenly distributed in the problem space regardless of its volume. Fuzzy i...

The security framework in Ad-hoc Networks (ANET) continues to attract the attention of researchers, although significant work has been accomplished already. Researchers last couple years have shown quite an improvement Identity Dependent Cryptography (IDC). Security ANET is hard attain due vulnerability links (Wireless). IDC encompasses Polynomial Interpolations (PI) such as Lagrange, curve-fit...