Louis Baker Rall
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Louis Baker Rallcomputer-science Degrees
Computer Science
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Numerical Analysis
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Louis Baker Rallmathematics Degrees
Mathematics
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Measure Theory
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#2571
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Computer Science Mathematics
Louis Baker Rall's Degrees
- PhD Mathematics Princeton University
- Bachelors Mathematics Princeton University
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(Suggest an Edit or Addition)Louis Baker Rall's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Automatic Differentiation: Techniques and Applications (1981) (718)
- Computational Solution of Nonlinear Operator Equations (1969) (488)
- Nonlinear Functional Analysis and Applications (1971) (285)
- Automatic differentiation (1981) (267)
- Convergence of the newton process to multiple solutions (1966) (122)
- The solution of characteristic value-vector problems by Newton's method (1968) (82)
- The Arithmetic of Differentiation (1986) (77)
- Quadratic equations in Banach spaces (1961) (59)
- A Note on the Convergence of Newton’s Method (1974) (56)
- Differentiation in PASCAL-SC: type GRADIENT (1984) (55)
- Adaptive, self-validating numerical quadrature (1987) (53)
- Error in Digital Computation (1965) (41)
- Theory of Linear Operators in Hilbert Space. Vol. I (N. I. Akhiezer and I. M. Glazman) (1962) (41)
- A Comparison of the Existence Theorems of Kantorovich and Moore (1980) (40)
- On complementary variational principles (1966) (40)
- Applications of Software for Automatic Differentiation in Numerical Computation (1980) (34)
- Mean Value and Taylor Forms in Interval Analysis (1983) (34)
- Pascal-SC: A computer language for scientific computation (1987) (34)
- Automatic error analysis (1981) (33)
- Annotated Bibliography on Generalized Inverses and Applications (1976) (30)
- Computational implementation of the multivariate Halley method for solving nonlinear systems of equations (1985) (28)
- Integration of Interval Functions (1981) (25)
- Differentiation and generation of taylor coefficients in PASCAL-SC (1983) (22)
- Numerical Integration and the Solution of Integral Equations by the Use of Riemann Sums (1965) (19)
- An introduction to automatic differentiation (1996) (17)
- Nonlinear Two Point Boundary Value Problems (Paul B. Bailey, Lawrence F. Shampine and Paul E. Waltman) (1970) (17)
- Convergence of Stirling's method in Banach spaces (1974) (15)
- Perspectives on Automatic Differentiation: Past, Present, and Future? (2006) (15)
- THE KANTOROVICH THEOREM AND ERROR ESTIMATES FOR NEWTON'S METHOD. (1970) (13)
- Improved Interval Bounds for Ranges of Functions (1985) (13)
- Elements of the Theory of Functions and Functional Analysis vol. I (A. N. Kolmogorov and S. V. Fomin); Metric and Normed Spaces vol. II (L. F. Boron, trans.); Measure—The Lebesgue Integral Hilbert Space (H. Kamel and H. Komm) (1962) (12)
- ERROR BOUNDS FOR ITERATIVE SOLUTIONS OF FREDHOLM INTEGRAL EQUATIONS (1955) (12)
- Integration of Interval Functions: II. The Finite Case (1982) (12)
- Optimal Implementation of Differentiation Arithmetic. (1986) (12)
- Automatic Generation of Taylor Series in Pascal-SC: Basic Operations and Applications to Ordinary Differential Equations. (1983) (10)
- Application of Interval Integration to the Solution of Integral Equations. (1980) (10)
- A theory of interval iteration (1982) (10)
- Computational Divided Differencing and Divided-Difference Arithmetics (2003) (10)
- An Introduction to the Scientific Computing Language Pascal-SC (Pascal for Scientific Computation). (1984) (10)
- PASCAL-SC, Wirkungsvoll programmieren, kontrolliert rechnen (1986) (9)
- Differentiation Arithmetics (1990) (9)
- Global Optimization Using Automatic Differentiation and Interval Iteration. (1985) (8)
- INTE: A UNIVAC 1108/1110 Program for Numerical Integration with Rigorous Error Estimation. (1975) (8)
- On the Uniqueness of Solutions of Quadratic Equations (1969) (8)
- Variational Methods in Mathematics, Science and Engineering (Karel Rektorys) (1980) (7)
- Perturbation methods for the solution of linear problems (1979) (7)
- A UNIVAC 1108 Program for Obtaining Rigorous Error Estimates for Approximate Solutions of Systems of Equations. (1972) (7)
- Representations of intervals and optimal error bounds (1983) (7)
- The Fredholm Pseudoinverse–An Analytic Episode in the History of Generalized Inverses (1976) (6)
- NEWTON: A GENERAL PURPOSE PROGRAM FOR SOLVING NONLINEAR SYSTEMS. (1967) (6)
- Algorithmic Differencing (2001) (6)
- Newton’s Method for the Characteristic Value Problem $Ax = \lambda Bx$ (1961) (5)
- Automatic Differentiation: Point and Interval (2009) (5)
- Early Automatic Differentiation: The Ch’in-Horner Algorithm (2007) (4)
- Solution of Nonlinear Systems of Equations (1973) (4)
- Quasilinearization and Nonlinear Boundary-Value Problems (R. E. Bellman and R. E. Kalaba) (1966) (4)
- Resolvent Kernels of Green’s Function Kernels and Other Finite-Rank Modifications of Fredholm and Volterra Kernels (1978) (4)
- Tools for Mathematical Computation (1991) (3)
- OPTIMIZATION OF INTERVAL COMPUTATION (1980) (3)
- Convergence of Stirling's method in Banach spaces (1975) (3)
- Interval methods for fixed-point problems (1987) (3)
- A quadratically convergent iteration method for computing zeros of operators satisfying autonomous differential equations (1976) (3)
- Iterative Solution of Nonlinear Equations in Spneod Variables (J. M. Ortega and W. C. Rheinboldt) (1974) (3)
- Gradient Computation by Matrix Multiplication (1996) (2)
- Interval bounds for stationary values of functionals (1982) (2)
- Solution of finite systems of equations by interval iteration (1982) (2)
- Error in digital computation : proceedings of an Advanced Seminar conducted by the Mathematics Research Center, United States Army, at the University of Wisconsin, Madison, October 5-7, 1964 (1965) (2)
- ReportsReview of introduction to interval computations, by Götz Alefeld and Jürgen Herzberger☆ (1986) (2)
- Interval Analysis: A New Tool for Applied Mathematics. (1981) (2)
- Numerics with automatic result verification (1993) (2)
- EFFICIENT USE OF NEWTON'S METHOD. (1964) (2)
- COMPUTABLE BOUNDS FOR SOLUTIONS OF INTEGRAL EQUATIONS (1985) (2)
- Current Issues in Computer Simulation. EDITED BY NABIL R. ADAM AND ALI DOGRAMACI. Academic (1979) (1)
- Automatic computation of gradients, Jacobians, Hessians, and applications to optimization (1981) (1)
- Interval Divided-Difference Arithmetic (2016) (1)
- Bounding Derivative Ranges (2009) (1)
- Resolvent kernels of Green's function kernels and other finite-rank modifications of Fredholm and Volterra kernels (1978) (1)
- The quadratic formula in Banach space (1956) (1)
- Computer Arithmetic in Theory and Practice (Ulrich W. Kulisch and Willard L. Miranker) (1983) (1)
- Evaluation of Functions, Gradients, and Jacobians (2003) (0)
- Programming and Utilizing Digital Computers (R. S. Ledley) (1963) (0)
- NEWTON'S METHOD FOR CHARACTERISTIC VALUEVECTOR PROBLEMS. (1964) (0)
- Numerical integration with regorous error estimation (1981) (0)
- A Review of Standard Pascal (1987) (0)
- Algorithmic Differentiation and Differencing (1999) (0)
- A Variant Kantororvich Theorem and High Accuracy Error Estimates in Newton's Method (2008) (0)
- Generation of Taylor coefficients (1981) (0)
- An Introduction to Pascal-SC (1987) (0)
- Problems for Solution: 4638-4642 (1955) (0)
- Strings and Text Processing (1987) (0)
- Examples of software for automatic differentiation and generation of Taylor coefficients (1981) (0)
- Additional notes of techniques, applications, and software (1981) (0)
- Numerical Computation with Validation (1988) (0)
- Error in digital computation : proceedings of a Symposium Conducted by the Mathematics Research Center, United States Army, at the University of Wisconsin, Madison, April 26-28, 1965 (1965) (0)
- Solving Problems with Pascal-SC (1987) (0)
- The problem of the minimum of a quadratic functional: by S. G. Mikhlin. (Russian trans. by A. Feinstein.) 155 pages, diagrams, 7 × 10 in. San Francisco, Calif., Holden-Day, Inc., 1965. Price, $8.95 (1965) (0)
- A Method for the Numerical Solution of Two-Point Boundary Value Problems Based on the Use of Volterra Integral. (1973) (0)
- Solution of Linear Integral Equations by the Use of Invariant Functions (1969) (0)
- Computable Error Bounds for the Nystroem Method. (1978) (0)
- Real Floating-Point Arithmetic—The Heart of a Scientific Programming Language (1987) (0)
- Validation of Numerical Computation (1988) (0)
- Nonlinear Mathematics (Thomas L. Saaty and Joseph Bram) (1966) (0)
- Functions and Operators with Arbitrary Result Types (1987) (0)
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