This category on scientific computing is based on my previous personal notes on the topic while studying for my EE major. I have rewritten the notes here for self reference.
What is scientific computing
It is a branch of applied mathematics. Involves solving mathematical problems by the use of algorithms and the assessment of the accuracies of the algorithm to the form of the problem. It is also known as Numerical computing.
It is important if one plans to use a computer for performing calculations and even in physical computing in embedded systems where math is performed on an observed variable such as temperature. A good use of this is in digital signal processing(DSP). Majority of scientific computing involves simplification of the problem at hand.
- Replacing non linear problems with linear problems.
- Replacing higher order systems with lower order systems
- Replacing complicated functions with simple functions such as polynomials.
- Replacing general matrices with matrices of a simpler form.
- Replacing infinite integrals with finite operations such as: Replacing integrals/infinite series with finite sums. Also includes replacing derivatives with finite difference equations.
- Replacing infinite dimensional space with a finite dimensional space.
How to solve by the general strategy
- Obtain an alternative version of the problem, or a class of problems easier to solve but preserves the solution in some sense.