Affine arithmetic

Affine arithmetic (AA) is a computer arithmetic which wis made tae improve the performance o interval arithmetic.

Background

Today, the interval arithmetic technology which wis made bi Sunaga^[1] & R. Moore^[2][3][4] is usit i many areas includin validatit numerics^[5]. But unfortunately, interval arithmetic is useless whan numerical computation is repeatit many times^[4]. Therefore, many experts have studiit hou tae overcome this weakness. Affine arithmetic is ane result o this movement.

Applications

Affine arithmetic is available i some interval arithmetic libraries like INTLAB^[6][7]. It is also usit i the followin fields:

• Electrical circuits^[8][9][10]
• Mixit signal systems^{[11][12][13][14]}
• Numerical methods for ordinary differential equations^[15]
• Optimization^[16][17]
• Power flow^{[18][19][20][21][22][23][24][25]}
• Root-findin algorithms^[26][27]

Improvements

Some experts are tryin tae improve affine arithmetic. Their results are known as the extendit affine arithmetic^[28][29][30] or modifiit affine arithmetic^[31][32].

Libraries

This a list o libraries thon supports affine arithmetic:

• kv^[33]
• Libaffa
• YalAA Archived 2021-01-27 at the Wayback Machine
• ASOL