Introduction to Numerical Methods (M-I-T)

• Square Roots via Newton's Method (PDF) (M-I-T)
• Floating-Point Arithmetic, the IEEE Standard (PDF) (M-I-T)
• Notes on the Accuracy of Naive Summation (PDF) (M-I-T)
• Backwards Stability of Recursive Summation (PDF) (M-I-T)
• Modern Differential Equations Solver Software: Where We Are and Where We're Headed (PDF - 2.4MB) (M-I-T)
• Householder Reflectors and Givens Rotations (PDF) (M-I-T)
• Classical vs. Modified Gram-Schmidt (M-I-T)
• Performance Experiments with Matrix Multiplication (PDF) (M-I-T)
• Ideal-Cache Terminology (PDF) (M-I-T)
• Experiments with Cache-Oblivious Matrix Multiplication (PDF) (M-I-T)
• Hessenberg Factorization (PDF) (M-I-T)
• Why Restarting Arnoldi/Lanczos is not Trivial (PDF) (M-I-T)
• Sparse Matrix Algorithms (PDF) (M-I-T)
• A Brief Overview of Optimization Problems (PDF) (M-I-T)
• Adjoint Methods (PDF) (M-I-T)
• Adjoint Methods and Sensitivity Analysis for Recurrence Relations (PDF) (M-I-T)
• Quasi-Newton Optimization: Origin of the BFGS Update (PDF) (M-I-T)
• Numerical Integration and the Redemption of the Trapezoidal Rule (PDF) (M-I-T)
• Fourier Cosine Series Examples (PDF) (M-I-T)
• Fast Fourier Transform and Fast Fourier Transform in the West (PDF - 2.6MB) (M-I-T)