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
.
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
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
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
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
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
1 edition published in 1981 in English and held by 27 WorldCat member libraries worldwide
PASCALSC : 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
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, roundoff, 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
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, roundoff, 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
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 semilocal 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)
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 semilocal 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 twopoint 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
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
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)
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)
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)
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)
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 57, 1964(
Book
)
2 editions published in 1965 in English and held by 4 WorldCat member libraries worldwide
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)
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)
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)
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)
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)
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 University of WisconsinMadison Mathematics Research Center Organizer of meeting
 Mathematics Research Center (United States. Army)
 University of Wisconsin
 United States Army
 Bohlender, Gerd Author
 University of WisconsinMadison Mathematics research center (Madison, Wis.). Organizer of meeting
 Mathematics Research Center
 Gray, Julia H. Author
 WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
 University of Wisconsin Mathematics research center
Associated Subjects
Banach spaces Boundary value problems Computer arithmetic Computer programming Convergence Differential calculusData processing Electronic digital computers EquationsNumerical solutions Error analysis (Mathematics) Functional analysis Green's functions Homotopy theory Integral equations Integral operators Invariants Iterative methods (Mathematics) Mathematics Matrices NewtonRaphson method Nonlinear functional analysis Nonlinear operators Numerical analysis Numerical integration Operator equations, Nonlinear Operator equationsNumerical solutions PascalSC (Computer program language) Polynomials Roundoff errors Univac computerProgramming