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Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions
TLDR
This paper presents convergence properties of the Nelder--Mead algorithm applied to strictly convex functions in dimensions 1 and 2, and proves convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2.
OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS
The path taken by a car with a given minimum turning radius has a lower bound on its radius of curvature at each point, but the path has cusps if the car shifts into or out of reverse gear. What is
Estimating Solutions of First Kind Integral Equations with Nonnegative Constraints and Optimal Smoothing
A method is presented for estimating solutions of Fredholm integral equations of the first kind, given noisy data. Regularization is effected by a smoothing term which is the $L^2 $-norm of the
Shift-Register Synthesis (Modulo m)
TLDR
The Berlekamp-Massey algorithm is extended to the case when the elements of the sequence are integers modulo m, where m is an arbitrary integer with known prime decomposition.
Inequalities and Positive-Definite Functions Arising from a Problem in Multidimensional Scaling
We solve the following variational problem: Find the maximum of E ∥ X−Y ∥ subject to E ∥ X ∥2 ≤ 1, where X and Y are i.i.d. random n-vectors, and ∥⋅∥ is the usual Euclidean norm on Rn. This problem
Orthonormal bases of exponentials for the n-cube
Any set that gives such an orthogonal basis is called a spectrum for . Only very special sets in R are spectral sets. However, when a spectrum exists, it can be viewed as a generalization of Fourier
Identification of stops and vowels for the burst portion of (p,t,k) isolated from conversational speech.
The stops /p t k/ were tested for identification in the context of /i a u/. The burst portions of initial and final stops were isolated from conversational speech through electronic gating circuitry.
Asymptotic Number of Roots of Cauchy Location Likelihood Equations
How many elements has Rn; how many roots are there? The standard maximum likelihood theory guarantees that one of the elements of Rn-the maximum likelihood estimate-is close to 0, and that all other
Identification of Stops and Vowels for the Burst Portion of /p, t, k/ Isolated from Conversational Speech
Stimulus segments (burst, and burst plus 100 msec of vowel) were isolated from words with initial and final /p,t,k/, and presented to listeners for identification. For the burst alone, initials were
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