Affine arithmetic

Affine arithmetic (AA) is a computer arithmetic which was made to improve the performance of interval arithmetic.

Background

Today, the interval arithmetic technology which was made by Sunaga^[1] and R. Moore^[2][3][4] is used in many areas including validated numerics.^[5] Unfortunately, interval arithmetic is useless when numerical computation is repeated many times.^[4] Therefore, many experts have studied how to overcome this weakness. Affine arithmetic is one result of this movement.

Applications

Affine arithmetic is available in some interval arithmetic libraries like INTLAB.^[6][7] It is also used in the following fields:

• Electrical circuits^[8][9][10]
• Mixed 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-finding algorithms^[26][27]

Improvements

Some experts are trying to improve affine arithmetic. Their results are known as the extended affine arithmetic^[28][29][30] or modified affine arithmetic.^[31][32]

Libraries

This a list of libraries that supports affine arithmetic:

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