dimitris kalamaras

mathematics, social network analysis, free software…

Tag: Pascal

Sparse Linear Systems Solver With SOR

This is a very simple Pascal program I wrote in mid 1990s, which solves a sparse NxN linear system using the Succesive Overrelaxation Method (SOR), which in turn is based on Gauss Seidel Method.
Both methods are iterative.

N is initially set at maximum …64.
You need the W factor for the SOR to complete successful. The theory assures us that it must be W=1.062.

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Tridiagonal Linear System Solver

This Pascal program is usefull in solving large tridiagonal linear systems. An example is the systems emerging from numerically integrating parabolic PDE’s by Finite Differences method.

It was ported to Turbo Pascal from a Fortran 77 program.
Its usage is very simple. All you have to do is to enter dimension of the system and the data, ie the three diagonals and the constant vector. Have fun…

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Turbo Editor

This is a simple text editor, called TED (Turbo EDitor). It opens text files or creates new ones in the same directory as the executable. It has a limit in the rows of the text file, but you can easily extend it by changing the appropriate variable. With small text files, ie less than 200 lines, it should work with them easily. The user interface is completely DOS oriented. Dont expect mouse support or any Hi-Tech GUI. It is just a small DOS program which was originally created to demonstrate string manipulation algorithms in Turbo Pascal. Thus, it provides you with actions like SEARCH string, DELETE string, INSERT string etc.
This program is the same algorithmically with CED, the text editor in C++ section.

Prime numbers’ generator

This is a Prime Numbers’ Generator from Integers up to 2,000,000,000, written in Turbo Pascal.
This program generates the prime numbers up to a given arithmetic limit, using 4 (four) different known methods. They are all based in modulo algebra. The methods are:

  1. This uses the mathematical definition of a prime number to generate them. A prime is only divided by 1 and himself. Disadvantage: The method is very slow.
  2. In this method, each number N is modulo divided only with the half of the numbers below it (N/2). Thus, the search is becoming faster than the first method.
  3. In the third method, a number, let N, is modulo divided only with the numbers up to sqrt{N}. As a result of that, the generation process is 10 times faster than the previous methods.
  4. The fourth method is the best of all. It is based on the 3rd method, only it bypass the sqrt{x} praxis, by modulo dividing each number N with the first, the second and the third prime number and then, if there is a residue, it modulo divides N with j, where j is an integer from j*j cdots N with step 2. The above trick has the eye-blink effect: the method generates primes (within a reasonable range) before you blink your eyes….:-)

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