Contents:

Part One: Nonlinear Equations. Lecture 1: By the Dawn's Early Light; Interval Bisection; Relative Error; Lecture 2: Newton's Method; Reciprocals and Square Roots; Local Convergence Analysis; Slow Death; Lecture 3: A Quasi-Newton Method; Rates of Convergence; Iterating for a Fixed Point; Multiple Zeros; Ending with a Proposition; Lecture 4: The Secant Method; Convergence; Rate of Convergence; Multipoint Methods; Muller's Method; The Linear-Fractional Method; Lecture 5: A Hybrid Method; Errors, Accuracy, and Condition Numbers. Part Two: Computer Arithmetic. Lecture 6: Floating-Point Numbers; Overflow and Underflow; Rounding Error; Floating-point Arithmetic; Lecture 7: Computing Sums; Backward Error Analysis; Perturbation Analysis; Cheap and Chippy Chopping; Lecture 8: Cancellation; The Quadratic Equation; That Fatal Bit of Rounding Error; Envoi. Part Three: Linear Equations. Lecture 9: Matrices, Vectors, and Scalars; Operations with Matrices; Rank-One Matrices; Partitioned Matrices; Lecture 10: Theory of Linear Systems; Computational Generalities; Triangular Systems; Operation Counts; Lecture 11: Memory Considerations; Row Oriented Algorithms; A Column Oriented Algorithm; General Observations on Row and Column Orientation; Basic Linear Algebra Subprograms; Lecture 12: Positive Definite Matrices; The Cholesky Decomposition; Economics; Lecture 13: Inner-Product Form of the Cholesky Algorithm; Gaussian Elimination; Lecture 14: Pivoting; BLAS; Upper Hessenberg and Tridiagonal Systems; Lecture 15: Vector Norms; Matrix Norms; Relative Error; Sensitivity of Linear Systems; Lecture 16: The Condition of Linear Systems; Artificial Ill Conditioning; Rounding Error and Gaussian Elimination; Comments on the Analysis; Lecture 17: The Wonderful Residual: A Project; Introduction; More on Norms; The Wonderful Residual; Matrices with Known Condition; Invert and Multiply; Cramer's Rule; Submission.Part Four: Polynomial Interpolation. Lecture 18: Quadratic Interpolation; Shifting; Polynomial Interpolation; Lagrange Polynomials and Existence; Uniqueness; Lecture 19: Synthetic Division; The Newton Form of the Interpolant; Evaluation; Existence; Divided Differences; Lecture 20: Error in Interpolation; Error Bounds; Convergence; Chebyshev Points. Part Five: Numerical Integration and Differentiation. Lecture 21: Numerical Integration; Change of Intervals; The Trapezoidal Rule; The Composite Trapezoidal Rule; Newton-Cotes Formulas; Undetermined Coefficients and Simpson's Rule; Lecture 22: The Composite Simpson's Rule; Errors in Simpson's Rule; Weighting Functions; Gaussian Quadrature; Lecture 23: The Setting; Orthogonal Polynomials; Existence; Zeros of Orthogonal Polynomials; Gaussian Quadrature; Error and Convergence; Examples; Lecture 24: Numerical Differentiation and Integration; Formulas From Power Series; Limitations; Bibliography.

Item type | Location | Call number | Copy | Status | Date due |
---|---|---|---|---|---|

BOOK | Mesa Lab | QA297 .S785 1996 (Browse shelf) | 1 | Available |

Includes bibliographical references (p. 187-189) and index.

Part One: Nonlinear Equations. Lecture 1: By the Dawn's Early Light; Interval Bisection; Relative Error; Lecture 2: Newton's Method; Reciprocals and Square Roots; Local Convergence Analysis; Slow Death; Lecture 3: A Quasi-Newton Method; Rates of Convergence; Iterating for a Fixed Point; Multiple Zeros; Ending with a Proposition; Lecture 4: The Secant Method; Convergence; Rate of Convergence; Multipoint Methods; Muller's Method; The Linear-Fractional Method; Lecture 5: A Hybrid Method; Errors, Accuracy, and Condition Numbers. Part Two: Computer Arithmetic. Lecture 6: Floating-Point Numbers; Overflow and Underflow; Rounding Error; Floating-point Arithmetic; Lecture 7: Computing Sums; Backward Error Analysis; Perturbation Analysis; Cheap and Chippy Chopping; Lecture 8: Cancellation; The Quadratic Equation; That Fatal Bit of Rounding Error; Envoi. Part Three: Linear Equations. Lecture 9: Matrices, Vectors, and Scalars; Operations with Matrices; Rank-One Matrices; Partitioned Matrices; Lecture 10: Theory of Linear Systems; Computational Generalities; Triangular Systems; Operation Counts; Lecture 11: Memory Considerations; Row Oriented Algorithms; A Column Oriented Algorithm; General Observations on Row and Column Orientation; Basic Linear Algebra Subprograms; Lecture 12: Positive Definite Matrices; The Cholesky Decomposition; Economics; Lecture 13: Inner-Product Form of the Cholesky Algorithm; Gaussian Elimination; Lecture 14: Pivoting; BLAS; Upper Hessenberg and Tridiagonal Systems; Lecture 15: Vector Norms; Matrix Norms; Relative Error; Sensitivity of Linear Systems; Lecture 16: The Condition of Linear Systems; Artificial Ill Conditioning; Rounding Error and Gaussian Elimination; Comments on the Analysis; Lecture 17: The Wonderful Residual: A Project; Introduction; More on Norms; The Wonderful Residual; Matrices with Known Condition; Invert and Multiply; Cramer's Rule; Submission.Part Four: Polynomial Interpolation. Lecture 18: Quadratic Interpolation; Shifting; Polynomial Interpolation; Lagrange Polynomials and Existence; Uniqueness; Lecture 19: Synthetic Division; The Newton Form of the Interpolant; Evaluation; Existence; Divided Differences; Lecture 20: Error in Interpolation; Error Bounds; Convergence; Chebyshev Points. Part Five: Numerical Integration and Differentiation. Lecture 21: Numerical Integration; Change of Intervals; The Trapezoidal Rule; The Composite Trapezoidal Rule; Newton-Cotes Formulas; Undetermined Coefficients and Simpson's Rule; Lecture 22: The Composite Simpson's Rule; Errors in Simpson's Rule; Weighting Functions; Gaussian Quadrature; Lecture 23: The Setting; Orthogonal Polynomials; Existence; Zeros of Orthogonal Polynomials; Gaussian Quadrature; Error and Convergence; Examples; Lecture 24: Numerical Differentiation and Integration; Formulas From Power Series; Limitations; Bibliography.

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