WorldCat Identities

Rall, Louis B.

Overview
Works: 41 works in 183 publications in 2 languages and 2,020 library holdings
Genres: Conference papers and proceedings  Periodicals 
Roles: Author, Editor
Classifications: QA3, 515.7
Publication Timeline
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Most widely held works by Louis B Rall
Nonlinear functional analysis and applications by Louis B Rall( Book )

31 editions published between 1971 and 2014 in English and Undetermined and held by 463 WorldCat member libraries worldwide

Nonlinear Functional Analysis and Applications
Error in digital computation by Louis B Rall( Book )

43 editions published in 1965 in English and Undetermined and held by 451 WorldCat member libraries worldwide

Computational solution of nonlinear operator equations by Louis B Rall( Book )

19 editions published between 1969 and 1979 in English and Undetermined and held by 436 WorldCat member libraries worldwide

Automatic differentiation : techniques and applications by Louis B Rall( Book )

17 editions published between 1981 and 2007 in English and German and held by 333 WorldCat member libraries worldwide

Automatic Differentiation: Techniques and Applications by Louis B Rall( )

1 edition published in 1981 in English and held by 27 WorldCat member libraries worldwide

PASCAL-SC : wirkungsvoll programmieren, kontrolliert rechnen by Gerd Bohlender( Book )

2 editions published in 1986 in German and held by 19 WorldCat member libraries worldwide

Software -- Programming Languages
INTE : a Univac 1108/1110 program for numerical integration with rigorous error estimation by Julia H Gray( Book )

5 editions published in 1975 in English and held by 10 WorldCat member libraries worldwide

By use of the concepts of interval analysis, one can construct methods for numerical integration which give rigorous bounds on errors due to imprecise data, round-off, and truncation, and also make possible the detection of the use of incorrect formulas. On the basis of parameters obtained from interval integration formulas, the calculation of numerical integrals can be optimized with respect to time and accuracy. Improved error bounds can also be obtained in certain cases by intersection of interval results. This paper describes a computational system of interval type which has been implemented as a computer program for the UNIVAC 1108/1110, using software previously developed at MRC for interval analysis and automatic differentiation. The program accepts integrands which are functions of a single variable, written as one or more ordinary FORTRAN statements. In addition to the variable of integration, these statements may include one or more parameters to be specified by the user, and the program may be used in interactive or batch mode
Error in digital computation; proceedings of an advanced seminar conducted by Louis B Rall( Book )

1 edition published in 1965 in English and held by 9 WorldCat member libraries worldwide

Convergence of Stirling's method in Banach spaces by Louis B Rall( Book )

4 editions published in 1972 in English and held by 5 WorldCat member libraries worldwide

A general class of iteration processes including Stirling's method is studied, and local and semi-local theorems are proved which show the quadratic convergence of Stirling's method under the assumptions of uniform boundedness and Lipschitz continuity of the Frechet derivative F' of the operator F. Comparisons between Stirling's and Newton's methods are given. (Author)
A method for the numerical solution of two-point boundary value problems based on the use of Volterra integral operators by H Fujita( Book )

4 editions published in 1973 in English and held by 4 WorldCat member libraries worldwide

Computational solution of nonlinear operator equations by Louis B Rall( )

1 edition published in 1969 in English and held by 4 WorldCat member libraries worldwide

Solution of linear integral equations by the use of invariant functions by Louis B Rall( Book )

4 editions published in 1968 in English and held by 4 WorldCat member libraries worldwide

A simple method is presented for the solution of linear integral equations. The relationship of this method to the replacement of an integral equation by an infinite system of equations and to the solution of integral equations by the use of characteristic functions (eigenfunctions) is shown, and its application is illustrated by a simple example. (Author)
Solution of abstract polynomial equations by iterative methods by Louis B Rall( Book )

4 editions published in 1968 in English and held by 4 WorldCat member libraries worldwide

Simple computational methods are given for solving a large class of nonlinear equations of polynomial type. (Author)
Davidenko's method for the solution of nonlinear operator equations by Louis B Rall( Book )

3 editions published in 1968 in English and held by 4 WorldCat member libraries worldwide

The theory and some applications of Davidenko's method for solving nonlinear equations are described. (Author)
Numerical Inversion of Green's Matrices by Louis B Rall( Book )

4 editions published in 1971 in English and held by 4 WorldCat member libraries worldwide

A simple method is presented for solving systems of equations with coefficient matrices having a structure similar to Green's functions. Inversion of such matrices and the calculation of their eigenvalues and eigenvectors is also considered. A numerical example is given. (Author)
Proceedings of an advanced seminar conducted by the Mathematics Research Center : Madison, October 5-7, 1964( Book )

2 editions published in 1965 in English and held by 4 WorldCat member libraries worldwide

Rates of convergence of Newton's method by Louis B Rall( Book )

4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide

Given an operator P in a Banach space X with Lipschitz continuous derivative P primed, it is shown that the existence of 1/(P primed (x + 1)) is necessary and sufficient to predict on the basis of the theorem of L.V. Kantorovic that the Newton sequence x sub (n + 1) = (x sub n) - P(x sub n)/(P primed(s sub n)) will converge to a solution x of the equation P(x) = o quadratically. Some examples are given of convergent Newton sequences for which convergence and the rate of convergence cannot be predicted by the Kantorovic theorem. (Author)
The Kantorovich theorem and error estimates for Newton's method by Louis B Rall( Book )

3 editions published in 1970 in English and held by 4 WorldCat member libraries worldwide

In this note the authors derive a simple recurrence relation for the best possible error estimates the Kantorovich theorem can give for Newton's method. This formulation has, as immediate consequences, all previously derived error estimates and some improved error estimates. (Author)
Error in digital computation( Book )

in English and held by 4 WorldCat member libraries worldwide

Convergence of the newton process to multiple solutions by Louis B Rall( Book )

3 editions published in 1966 in English and held by 3 WorldCat member libraries worldwide

The slow convergence of Newton's method to multiple solutions of scalar and finite systems of equations is characterized, and a corrected Newton procedure having quadratic convergence is developed. The results are extended to a class of nonlinear operator equations. (Author)
 
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Audience level: 0.65 (from 0.61 for Nonlinear ... to 0.98 for Error in d ...)

Automatic differentiation : techniques and applications
Alternative Names
Rall, L. B.

Languages
English (147)

German (3)

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