# THE ITERATIVE METHOD

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DIRECTION-CODE-MUSIC-GFX:

LEONARDOWORX

Case studies about iterative method and

how can it be connected to generative life.

It's about how math and physic can be the key for explaining human life and perception, even the feelings we can not quantify, like love, that goes beyond time and space dimensions.

NOTE:

This project started developing code functions in Max/Msp and Processing using Arrays and the "for" instruction.

After i decided to connect all research i made (studying physic books, TED talks, M.I.T. documents) in one project, trying to enhance the conncetion between these studies and my life experience.

ABOUT ITERATIVE METHOD:

In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method. An iterative method is called convergent if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common.

In the problems of finding the root of an equation (or a solution of a system of equations), an iterative method uses an initial guess to generate successive approximations to a solution. In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution.

Iterative methods are often the only choice for nonlinear equations. However, iterative methods are often useful even for linear problems involving a large number of variables (sometimes of the order of millions), where direct methods would be prohibitively expensive (and in some cases impossible) even with the best available computing power.

DIRECTION-CODE-MUSIC-GFX:

LEONARDOWORX

Case studies about iterative method and

how can it be connected to generative life.

It's about how math and physic can be the key for explaining human life and perception, even the feelings we can not quantify, like love, that goes beyond time and space dimensions.

NOTE:

This project started developing code functions in Max/Msp and Processing using Arrays and the "for" instruction.

After i decided to connect all research i made (studying physic books, TED talks, M.I.T. documents) in one project, trying to enhance the conncetion between these studies and my life experience.

ABOUT ITERATIVE METHOD:

In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method. An iterative method is called convergent if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common.

In the problems of finding the root of an equation (or a solution of a system of equations), an iterative method uses an initial guess to generate successive approximations to a solution. In contrast, direct methods attempt to solve the problem by a finite sequence of operations. In the absence of rounding errors, direct methods would deliver an exact solution.

Iterative methods are often the only choice for nonlinear equations. However, iterative methods are often useful even for linear problems involving a large number of variables (sometimes of the order of millions), where direct methods would be prohibitively expensive (and in some cases impossible) even with the best available computing power.