Category: Memoirs of James Pate Williams Jr
Blog Entry Thursday, June 20, 2024 (c) James Pate Williams, Jr. Some 3D Graphs (Application Edited 2024)
Blog Entry Tuesday, June 18, 2024 (c) James Pate Williams, Jr. FreeLIP Computation of Euler Numbers and Tangent Numbers
FreeLIP is a free large integer package solely created by Professor Emeritus Arjen K. Lenstra of the Number Field Sieve fame. He developed FreeLIP while he was an employee of AT&T – Lucent in the late 1980s. His copyright notice in the header file, lip.h, states copyright from 1989 to 1997. I have been using this excellent number theoretical package since the late 1990s. See the paper by Donald E. Knuth and Thomas J. Buckholtz for the formula for Tangent Numbers. I can’t remember where I got the Euler Numbers recurrence relation. I wrote a C# application in 2015 for computing Euler Numbers. The code below is in the vanilla C computer language. Excellent resources for the Euler and tangent numbers also known as zag numbers are:
Blog Entry Sunday, June 16, 2024 (c) James Pate Williams, Jr. Chapter 4 Matrices and Systems of Linear Equations from a Textbook by S. D. Conte and Carl de Boor
Blog Entry Friday, June 14, 2024 (c) James Pate Williams, Jr.
For the last week or so I have been working my way through Chapter 3 The Solution of Nonlinear Equations found in the textbook “Numerical Analysis: An Algorithmic Approach” by S. D. Conte and Carl de Boor. I also used some C source code from “A Numerical Library in C for Scientists and Engineers” by H. T. Lau, PhD. I implemented twenty examples and exercises from the previously mentioned chapter.
Blog Entry Friday, June 7, 2024, (c) James Pate Williams, Jr. A Nice Integral
Blog Entry June 5-7, 2024, (c) James Pate Williams, Jr. All Applicable Rights Reserved Chapter 7 Example and Some Exercises from “Numerical Analysis: An Algorithmic Approach (c) 1980 by S. D. Conte and Carl de Boor (Numerical Differentiation and Numerical Integration)
Blog Entry June 3-4, 2024, (c) James Pate Wiliams, Jr., Solution of Tridiagonal Matrix Problems
The first solution is from the textbook, Elementary Numerical Analysis: An Algorithmic Approach (c) 1980 by S. D. Conte and Carl de Boor. I translated the FORTRAN code to vanilla C using Visual Studio 2019 Community Version. The second solution is from Boundary Value Problems Second Edition (c) 1979 by David L. Powers. It solves a simple second order linear ordinary differential equation using the finite element difference equation method.
Numerical Explorations 