Browsing by Subject "Approximation theory"
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Item A deterministsic numerical method for solutions of first-passage time problems(Texas Tech University, 1996-12) Sharp, Wyatt D.In this research, a new deterministic numerical procedure for first passage time problems is introduced, analyzed, and numerically tested. In this procedure, the Green's function solution to the forward Kolmogovorov equation is approximated for a small time step. The reliability function is then approximated by recursively and numerically solving an iterated integral whose integrand involves the approximate Green's function. The reliability function, which solves the backward Kolmogorov equation, yields the probability distribution of first passage times, and hence the expected exit time. The error analysis is shown for the one dimensional case and can be modified for higher dimensions. Three numerical examples are given. Two of the examples are two dimensional problems which have been given special attention by other investigators [2, 10] because of their computational difficulty.Item Acceleration of quasi-Monte Carlo approximations(Texas Tech University, 2001-05) Severino, Joseph S,In this paper, a new method is presented for numerically approximating integrals using quasi-Monte Carlo sequences. By applying a least-squares smoothing procedure to the sequences, a faster rate of convergence is achieved thus reducing the number of nodes required for the same degree of accuracy. This acceleration method is applied to four particular integrals in a variety of dimensions. The first integral is a smooth exponential function and the second has a discontinuous integrand. The last two integrals deal with specific problems in mathematical finance. One computes the price for a European call option, while the other finds the present value of a mortgage-backed security over thirty years.Item Adaptive critic designs and their applications(Texas Tech University, 1997-12) Prokhorov, Danil VNOT AVAILABLEItem Applications of matrix theory to approximation theory(Texas Tech University, 1999-08) Butler, Leah JoanneIn this paper, we examine the relationship between the eigenvalues of the arbitrary sum of n rank 1 matrices and the eigenvalues of the summands. For n = 2. 3. and 4. We develop a polynomial, p, which annihilates the matrix which is the sum of n rank 1 matrices. Since the minimal polynomial is a factor of this annihilator polynomial, then the eigenvalues of this sum are roots of p. We conjecture that his form we creatcnl works for arbitrary n. Any rank 1 matrix may be written as the product of a column vector and a row vector. The coefficients of the polynomial we created are formed using only combinations of these rows and columns. We examine conditions which imply that our annihilator polynomial is exactly the characteristic polynomial of the sum. This gives the desired relationship between the eigenvalues of the individual rank 1 matrices and the eigenvalues of the sum.Item Approximation algorithms for NP-hard clustering problems(2002) Mettu, Ramgopal Reddy; Plaxton, C. GregItem Approximations to the noncentral Chi-square and noncentral F distributions(Texas Tech University, 1978-12) Weston, Bill RandallNot availableItem Checking the censored two-sample accelerated life model using integrated cumulative hazard difference(Texas Tech University, 2004-08) Lee, Seung-HwanIn this dissertation, soma lack-of-fit tests will be discussed for the censored two-sample accelerated life model. Conventional scale estimators with two-sample censored data such as rank-based estimators and minimum distance estimators have difficulties to apply easily due to the fact that their asymptotic variances involve the unknown density, or they require soma strict conditions. The object of this work is to provide an asymptotically equivalent martingale-based stochastic process of some estimating functions, which is easier to apply than existing methods from the literature. An extreme value of the observed process compared with simulated realizations of the approximation process would indicate the model misspecifications. The approximation process involving the martingale structure can be achieved through some approximation procedures of the observed process under the two-sample scale model. The p-value applied to the approximation of the observed process leads to the construction of the lack-of-fit tests. Comparison of the processes enables one to get some information visually from the graph about how the model is misspecified.Item Comparisons of Approximate F Test and A Procedure for the Development of An Alternative.(Texas Tech University, 1974-08) Keenum, Barbara JaneNot Available.Item Deterministic and stochastic discrete-time epidemics with spatial considerations(Texas Tech University, 1998-05) Burgin, Amy Marie BlackstockNot availableItem Interpolation and approximation in the space of Dirichlet polynomials(Texas Tech University, 1989-05) Brown, James FNot availableItem Monotonio polynomial approximation(Texas Tech University, 1971-05) Whitmore, Roy WalterNot availableItem On Edgeworth expansions with unknown cumulants(Texas Tech University, 1972-08) Coberly, William ArthurNot availableItem On properties of the zeros of the Cesàro approximants to outer functions(Texas Tech University, 1998-05) Wheeler, WilliamIn this paper, we will be concerned with determining properties of the zeros of the Cesaro sums for a fairly general class of outer functions. The class of outer functions that we will consider have positive monotonically decreasing coefficients. Let M be the set of functions analytic in D with positive monotonically decreasing coefficients in their series expansion.Item Optimal control of dynamic systems and its application to spline approximation(Texas Tech University, 1996-08) Agwu, Nwojo NnannaGenerally, classical polynomial splines tend to exhibit unwanted undulations. In this work, we discuss a technique, based on control principles, for eliminating these undulations and increasing the smoothness properties of the spline interpolants. We give a generalization of the classical polynomial splines and show that this generalization is, in fact, a family of splines that covers the broad spectrum of polynomial, trigonometric and exponential splines. A particular element in this family is determined by the appropriate control data. It is shown that this technique is easy to implement. Several numerical and curve-fitting examples are given to illustrate the advantages of this technique over the classical approach. Finally, we discuss the convergence properties of the interpolant.Item Parametric approximation of data using orthogonal distance regression splines(Texas Tech University, 2000-08) Franklin, Scott R.Not availableItem Piecewise isoplanatic approximation in space-variant processing(Texas Tech University, 1985-05) Lin, Shing-hongNot available