Numerical integration of nonlinear differential equations by use of rational approximation Final report, 15 Jan. 1965 - 14 Jul. 1967
Numerical integration of nonlinear differential equations by use of rational approximation
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Numerical integration of nonlinear differential equations by use of rational approximation
Rational approximation of generalized Duffing equation, damped mass spring oscillator equation and generalized second order Riccati equation
This article shows how rational analysis can be used to minimize learning cost for a general class of statistical learning problems. We discuss the factors that influence learning cost and show that the problem of efficient learning can be cast as a resource optimization problem. Solutions found in this way can be significantly more efficient than the best solutions that do not account for these factors. We introduce a heuristic learning algorithm that approximately solves this optimization problem and document its performance improvements on synthetic and real-world problems.
Linear fractional transformation for obtaining rational approximations to response of physical system defined by second order nonlinear differential equation with constant coefficients
Equivalence of irreducible realization in control theory and degree of rational matrix in network theory
Rational approximations to solution of second order nonlinear Ricatti equation, using linear transformations - differential equations and operational calculus
Linear transformation to obtain rational approximation to response of physical system described by nonlinear differential equation including Duffing equation as special case
Continued fraction rational approximations to solution of second-order nonlinear equation, including Ricatti equations treated by Merkes, Scott and Fair
Rational approximations to incomplete elliptic integral of first and second kinds derived by main diagonal Pade approximations
Rational approximations and solution of control theory problems involving Ricatti equations
Closed form rational approximations to Tricomi psi function
Computer method for determination of rational functions using sums of exponential approximations
Tabulation of high accuracy gamma function values for some rational arguments, noting applications to Gaussian quadrature formulas, fractional Bessel functions and Airy functions
Rational approximation for coefficients used in calculating hydrogenic photoionization Gaunt factors
Explicit inverse Fourier transformation of rational function with new theorem
Minimization techniques using rational approximations
Realization theory of rational transfer matrices presented as fundamental algebraic objects in theory of finite, constant linear systems
Noniterative method of obtaining rational forms as approximations to functions for power series expressions using Tchebycheff polynomial properties for improving accuracy