The computer program Rts, which is posted on this website, is a collection of models and methods, i.e., numbers and algorithms. This means that you can introduce new models and new methods without changing the existing code. This page makes available our “library” of methods, i.e., the algorithms implemented in Rts. The study of algorithms is interesting and certainly timely. Elon Musk suggests that artificial intelligence can become a danger to the public and Yuval Noah Hari discusses the role of algorithms, including the ones in your brain, in the book Homo Deus. The word “algorithm” stems not from Al Gore, who admittedly promoted the public use of ARPANET, which is now the Internet, but rather the Persian mathematician Muhammad bin Musa al-Khwarizmi who was born in 780 and worked at the House of Wisdom in Baghdad. However, the earliest algorithm is perhaps that of Euclid, born in 335 BC, who devised a systematic approach for determining the greatest common divisor of two integers. These days algorithms are implemented on the computer and in our group we use the C++ language together with Qt. Some material on getting started with C++ and Qt as well as some information on C++ programming is provided in those links.

**LINEAR SOLVERS**

- Input file with linear solvers
- Determinant and matrix inversion
- RMatrixInverseLinearSolver.h / RMatrixInverseLinearSolver.cpp
- Decomposition and substitution
- Classname.h / Classname.cpp
- Cholesky Decomposition
- Classname.h / Classname.cpp

**1D OPTIMIZATION & ROOT-FINDING**

- Bisection Algorithm
- Classname.h / Classname.cpp
- 1D Newton-Raphson Algorithm
- Classname.h / Classname.cpp
- Secant Algorithm
- Classname.h / Classname.cpp
- Golden Section Algorithm
- Classname.h / Classname.cpp

**EIGEN SOLVERS**

**OPTIMIZATION ALGORITHMS**

**OPTIMIZATION SEARCH DIRECTIONS**

**DIRECT OPTIMIZATION ALGORITHMS**

**NUMERICAL INTEGRATION**

**TIME INTEGRATION**

**NETWORK ALGORITHMS**

**MESH GENERATION**

**STRUCTURAL ASSEMBLY**

**MATERIAL MODELS**

**CYCLE COUNTING**

**SAMPLING**

**RANDOM NUMBER GENERATORS**

**INTERPOLATION**

**INFERENCE**

**FOURIER TRANSFORMS**

**SORTING**

We are playing around with the idea of having a discussion forum on each of these pages. If we post the individual models and methods, and then engage in discussions about them, would that improve the numbers and algorithms over time? Let’s see. Please feel free to leave comments below.

This is a test reply to the first message on this page…