- A Spectral Method for Elliptic Equations: The Dirichlet Problem
- On the Numerical Solution of Some Semilinear Elliptic Problems II K. Atkinson, Iowa City and A. Sommariva, Padua
- USER'S GUIDE TO A BOUNDARY ELEMENT PACKAGE FOR SOLVING INTEGRAL
- THE NUMERICAL SOLUTION OF A NONLINEAR BOUNDARY INTEGRAL
- NUMERICAL INTEGRATION How do you evaluate
- GENERAL ERROR FORMULA In general,
- JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS
- Solving a Single Layer Integral Equation On Surfaces in R3
- RESOURCES IN NUMERICAL ANALYSIS Kendall E. Atkinson
- A Discrete Galerkin Method for a Hypersingular Boundary Integral Equation
- MATLAB NOTES Matlab designed for numerical computing.
- LINEAR SYSTEMS Consider the following example of a linear system
- NUMERICAL METHODS FOR ODEs Consider the initial value problem
- DIFFERENTIAL EQUATIONS A principal model of physical phenomena.
- INTERPOLATION Interpolation is a process of finding a formula (often
- NUMERICAL ANALYSIS: This refers to the analysis of mathematical problems by numerical means, es-
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- THE EIGENVALUE PROBLEM Let A be an n n square matrix. If there is a number
- NUMERICAL ANALYSIS KENDALL E. ATKINSON
- PIECEWISE POLYNOMIAL COLLOCATION FOR BOUNDARY INTEGRAL EQUATIONS
- PROPAGATION OF ERROR Suppose we are evaluating a function f(x) in the ma-
- CORRECTIONS TO Theoretical Numerical Analysis
- Corrections of K. Atkinson and W. Han, Theoretical Numerical Analysis
- BINARY INTEGERS A binary integer x is a finite sequence of the digits 0
- CALCULATION OF FUNCTIONS Using hand calculations, a hand calculator, or a com-
- problem exactly in one pass; instead, solve it approximately, then iterate. Multigrid methods, perhaps the most important development in numerical computation in the past twenty years,
- Advances in Computational Mathematics 12 (2000) 151174 151 A fast matrixvector multiplication method for solving the
- A Personal Perspective on the History of the Numerical Analysis of Fredholm Integral
- Modelling a Road Using Spline Interpolation Kendall Atkinson
- NUMERICAL INTEGRATION: ANOTHER APPROACH
- A SPECTRAL METHOD FOR THE EIGENVALUE PROBLEM FOR ELLIPTIC EQUATIONS
- GAUSSIAN ELIMINATION -REVISITED Consider solving the linear system
- Electronic Transactions on Numerical Analysis. Volume 11, pp. 94-120, 2000.
- The Numerical Solution of Boundary Integral Kendall E. Atkinson
- Solving Fredholm Integral Equations of the Second Kind in Matlab
- Electronic Transactions on Numerical Analysis. Volume 17, pp. 206-217, 2004.
- A Spectral Method for Elliptic Equations: The Neumann Problem
- On the norm of the hyperinterpolation operator on the unit disk and its use for the solution of
- VITA -KENDALL E. ATKINSON April 3, 2011
- June 19, 2011 BIBLIOGRAPHY
- problem exactly in one pass instead, solve it approximately, then iterate. Multigrid methods, perhaps the most important development in numerical computation in the past twenty years,
- THE TAYLOR POLYNOMIAL ERROR FORMULA Let f(x) be a given function, and assume it has deriv-
- COMPUTING ANOMALIES These examples are meant to help motivate the study
- ROOTFINDING We want to find the numbers x for which
- ROOTFINDING : A PRINCIPLE We want to find the root of a given function f(x).
- FIXED POINT ITERATION We begin with a computational example. Consider
- MULTIPLE ROOTS We study two classes of functions for which there is
- ERROR IN LINEAR INTERPOLATION Let P1(x) denote the linear polynomial interpolating
- BEST APPROXIMATION Given a function f(x) that is continuous on a given
- CHEBYSHEV POLYNOMIALS Chebyshev polynomials are used in many parts of nu-
- TRAPEZOIDAL METHOD ERROR FORMULA
- NUMERICAL DIFFERENTIATION There are two major reasons for considering numeri-
- ESTIMATION OF ERROR Let bx denote an approximate solution for Ax = b;
- ITERATION METHODS These are methods which compute a sequence of pro-
- LEAST SQUARES DATA FITTING Experiments generally have error or uncertainty in mea-
- EXAMPLE OF ONE-STEP METHOD Consider solving
- SYSTEMS OF ODES Consider the pendulum shown below. Assume the rod
- TWO-POINT BVP Consider the two-point boundary value problem of a
- THE NUMERICAL SOLUTION OF INTEGRAL EQUATIONS OF THE
- Bibliography 1] M. Abramowitz and I. Stegun, editors (1965) Handbook of Mathematical
- Series Preface vii 1 Linear Spaces 1
- Appl. Num. Anal. Comp. Math. 1, No. 1, 3 22 (2004) / DOI 10.1002/anac.DOIsuffix Analytic Evaluation of Collocation Integrals for the Radiosity
- THE SECANT METHOD Newton's method was based on using the line tangent
- SYSTEMS OF NONLINEAR EQUATIONS Widely used in the mathematical modeling of real world
- SOME DEFINITIONS Let xT denote the true value of some number, usually
- THE NUMERICAL SOLUTION OF INTEGRAL EQUATIONS OF THE
- SOLVING LINEAR SYSTEMS We want to solve the linear system
- Electronic Transactions on Numerical Analysis. Volume 20, pp. 104-118, 2005.
- JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS
- PIECEWISE POLYNOMIAL INTERPOLATION Recall the examples of higher degree polynomial in-
- Matrices are rectangular arrays of real or complex numbers. With them, we define arithmetic operations
- SIAM J. MATH. ANAL. Vol. 5, No. 5, October 1974
- EVALUATING A POLYNOMIAL Consider having a polynomial
- Robust and Efficient Computation of the Closest Point on a Spline Curve
- CORRECTIONS AN INTRODUCTION TO NUMERICAL ANALYSIS, 2ND ED.
- JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS
- LEAST SQUARES APPROXIMATION Another approach to approximating a function f(x)
- Bibliography [1] M. Abramowitz and I. Stegun, editors (1965) Handbook of Mathematical
- A NEAR-MINIMAX APPROXIMATION METHOD Let f(x) be continuous on [a, b] = [-1, 1]. Consider
- MULTISTEP METHODS All of the methods we have studied until now are ex-
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- How should we compute a sum S = a1 + a2 + + an
- NUMERICAL STABILITY; IMPLICIT METHODS
- Electronic Transactions on Numerical Analysis. Volume 17, pp. 133-150, 2004.
- Electronic Transactions on Numerical Analysis. Volume 23, pp. 219-250, 2006.
- A Spectral Method for Elliptic Equations: The Neumann Problem
- Arc-Length Parameterized Spline Curves for Real-Time Simulation
- CORRECTIONS TO Elementary Numerical Analysis