Author: jamespatewilliamsjr

My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.

Comparison of Linear Systems Applications in C# and C++ by James Pate Williams, Jr.

Back in 2017 I created a C# application that implemented the direct methods: Cholesky decomposition, Gaussian elimination with partial pivoting, LU decomposition, and simple Gaussian elimination. The classical iterative methods Gauss-Seidel, Jacobi, Successive Overrelaxation, and gradient descent were also implemented along with the modern iterative methods: conjugate gradient descent and Modified Richardson’s method. Recently I translated the C# code to C++. I used the following test matrices: Cauchy, Lehmer, Pascal, and other. Below are some results. As is apparent the C++ runtimes are faster than the C# execution times.

linearsystems-resultsDownload

Richardson Method Translated from C Source Code to C# by James Pate Williams, Jr.

The Richardson Method is called before eliminating the system of linear equations.

Added elimination results from a vanilla C program and a C# application.

These results are not in total agreement with H. T. Lau’s results.

Finite Difference Method for Solving Second Order Ordinary Differential Equations by James Pate Williams, Jr.

My reference is Numerical Analysis: An Algorithmic Approach 3rd Edition by S. D. Conte and Carl de Boor Chapter 9.1.

My 1988 Commodore Amiga 2000 Is Still Functioning by James Pate Williams, Jr.

On Friday September 8, 2023, I setup my thirty-five-year-old personal computer which is a Commodore Amiga 2000. My father bought the computer for me on Saturday, April 30, 1988. It still works although the Commodore 1084 RGB color display has a non-functional power button. My remedy for the problem was to Scotch tape the power button in the “On” position. I have an Amiga BASIC by Microsoft manual and software, a Modula-2 compiler, Motorola MC68000 macro-assembly language software, and a Pecan UCSD Pascal compiler. The Amiga was the first multimedia personal computer. In May 1988 I created two Amiga BASIC programs: a keyboard emulator and a primitive computer-generated music program that used three types of noise namely Brownian, fractal, and white noise. I used the computer extensively in the years 1988 to 1994. In December 1994 my mother and older sister purchased a mom-and-pop store Microsoft-Intel personal computer.

Euler’s Method and Runge-Kutta 4 Algorithm for Numerically Solving an Ordinary Differential Equation by James Pate Williams, Jr.

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_225_Differential_Equations/3%3A_Numerical_Methods/3.1%3A_Euler’s_Method

I added the Runge-Kutta 4 algorithm found in Numerical Analysis: An Algorithmic Approach Third Edition by S. D. Conte and Carl de Boor. I also added a multistep method, the Adams-Bashforth Method.

Estimated Babe Ruth 1921 Homerun Parameters by James Pate Williams, Jr.

“Babe Ruth is generally considered the owner of the record for the longest home run in MLB history with a 575-foot bomb launched at Navin Field in Detroit in 1921.” – https://www.msn.com/en-us/sports/mlb/what-is-the-longest-home-run-in-mlb-history/ar-AA1dGwlZ

As you can see, I estimated the pitch velocity at 90 miles per hour and Babe Ruth’s (Sultan of Swing) at 90 miles per hour also. My analytic calculations yield a range of the baseball’s trajectory as about 576 feet.