Frank Stenger

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Let AA A A be a triangle with vertices at A1, A2 and A3. The process of "bisecting AA A A is defined as follows. We first locate the longest edge, A'Ai+i of AA 1A2A3 where A'+3 = Al, set D = (A' + Ai+l)/2, and then define two new triangles, AA'DAi+2 and ADAi+1Ai+2. Let Aqq be a given triangle, with smallest interior angle a > 0. Bisect AQ0 into two new(More)
Contents Abstract Sinc approximation methods excel for problems whose solutions may have singularities, or innnite domains, or boundary layers. This article summarizes results obtained to date, on Sinc numerical methods of computation. Sinc methods provide procedures for function approximation over bounded or unbounded regions, encompassing interpolation,(More)
This paper explains how to directly calculate a sufficient number of electronic vote counts (either precinct vote counts or DRE machine counts) to audit – count manually in order to detect an amount of electronic miscount that could wrongfully alter an election outcome. Vote count audits of fixed 1 or 2% of electronic counts provide no confidence that(More)
This paper gives a brief review of Sinc methods, with emphasis on the matrices of Sinc methods. A novel procedure is presented, based on Sinc convolution, for solving a Poisson problem over a rectangular region. Although some of the work of Gragg and Reichel may already be applied to the solution of Sinc{matrix problems, this paper also points to new(More)
This paper gives explicit rational functions for interpolating and approximating functions on the intervals [-1,1], [0, oo], and [-oo, oo]. The rational functions are linear in the functions to be approximated, and they have preassigned poles. The error of approximation of these rationals is nearly as small as the error of best rational approximation with(More)
We develop a numerical method based on Sine functions to obtain an approximate solution of a one-dimensional Cauchy singular integral equation (CSIE) over an arbitrary, smooth, open arc L of finite length in the complex plane. At the outset, we reduce the CSIE to a Fredholm integral equation of the second kind via a regularization procedure. We then obtain(More)
This paper describes an algorithm for the solution of a system of nonlinear equations F(X) --O, where 0 = (0 . . . . . 0) ~ R", and F is a gwen continuous transformation of n-dimensional simplex S into R"(n >_ 2) The program is based on computation of the topological degree ((leg) of a mapping and a slmplex-b~sectlon scheme. The algorithm is primarily(More)