International business machines corporation (20240176843). SOLVING SYSTEMS OF LINEAR EQUATIONS USING MIXED PRECISION simplified abstract

SOLVING SYSTEMS OF LINEAR EQUATIONS USING MIXED PRECISION

Organization Name

international business machines corporation

Inventor(s)

Tayfun Gokmen of Briarcliff Manor NY (US)

Vasileios Kalantzis of White Plains NY (US)

Shashanka Ubaru of Ossining NY (US)

Lior Horesh of North Salem NY (US)

SOLVING SYSTEMS OF LINEAR EQUATIONS USING MIXED PRECISION - A simplified explanation of the abstract

This abstract first appeared for US patent application 20240176843 titled 'SOLVING SYSTEMS OF LINEAR EQUATIONS USING MIXED PRECISION

Simplified Explanation

The abstract describes a method of computation that involves receiving a system of linear equations and computing a solution using a flexible iterative algorithm. The computation process includes identifying the most computationally expensive operation for each iteration, converting it to a low precision format, executing it in low precision, performing other operations in high precision, and finally returning the solution to the requesting device.

• The method involves receiving a system of linear equations.
• The solution is computed using a flexible iterative algorithm.
• The most computationally expensive operation is identified for each iteration.
• The identified operation is mapped to a low precision format.
• The operation is executed in low precision while other operations are performed in high precision.
• The solution is then returned to the requesting device.

Potential Applications

This technology could be applied in various fields such as:

• Scientific computing
• Engineering simulations
• Financial modeling

Problems Solved

This technology helps in:

• Improving computational efficiency
• Reducing computational resources required
• Enhancing accuracy of solutions

Benefits

The benefits of this technology include:

• Faster computation of solutions
• More efficient use of computational resources
• Improved accuracy in results

Potential Commercial Applications

This technology could be commercially applied in:

• Software for scientific and engineering calculations
• Financial analysis tools
• Cloud computing services

Possible Prior Art

One possible prior art for this technology could be:

• Previous methods of iterative algorithms for solving linear equations.

How does this method compare to traditional methods of solving linear equations?

This article does not provide a direct comparison between this method and traditional methods of solving linear equations. It would be interesting to know the specific advantages and disadvantages of this approach compared to more conventional techniques.

What are the potential limitations of implementing this flexible iterative algorithm in real-world applications?

The article does not address any potential limitations or challenges that may arise when implementing this flexible iterative algorithm in practical scenarios. Understanding these limitations could provide valuable insights into the feasibility and scalability of this technology.

Original Abstract Submitted

a method of computation includes receiving, by a requesting device, a system of linear equations, and computing a solution to the system of linear equations by a flexible iterative algorithm. the computing includes, for each iteration, determining a most computationally expensive operation of the iteration, mapping the most expensive operation to a low precision format, performing the most expensive operation according to a low precision, performing other operations of the iteration according to a high precision, and returning the solution to the requesting device.