APPROXIMATE COMPUTATIONAL COMPLEXITY

IN NUMERICAL SIMULATION

Abstract:

Present-day computational mathematics tries to overcome the boundaries beset by time (of calculation) and space (of memory allocation).  To this end, novel strategies have been identified in order to help researchers devise efficient algorithms.  One particular computational strategy, which can be termed approximated computational complexity, is based on relaxing some of the mathematical constraints, defining the calculation, in order to find approximated solutions of the original problem.

Such a strategy has found a success application in molecular dynamics simulation. A few relevant examples, taken from condensed matter physics, will be discussed.

It is also surmised that approximated computational complexity can be applied not only to algorithms but even to abstract theories so that a novel form of theory (which may be termed ‘computer theory’) is originated.

While not describing the real world, ‘computer theories’ exist with full legitimacy on the calculator.

One recent example of a ‘computer theory’ is provided by quasi-Hamiltonian dynamics, whose potential has, perhaps, not been fully exploited yet.

Some applications do classical and quantum systems are discussed.