18179411. SOLVING SYSTEMS OF LINEAR EQUATIONS USING MIXED PRECISION simplified abstract (INTERNATIONAL BUSINESS MACHINES CORPORATION)

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 18179411 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 algorithm determines the most computationally expensive operation for each iteration, maps it to a low precision format, performs the operation in low precision, and executes other operations in high precision before 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 algorithm identifies the most computationally expensive operation for each iteration.
• The most expensive operation is mapped to a low precision format.
• The operation is performed in low precision, while other operations are done in high precision.
• The final solution is returned to the requesting device.

Potential Applications

This technology could be applied in various fields such as:

• Scientific computing
• Financial modeling
• Machine learning algorithms

Problems Solved

This technology addresses the following issues:

• Efficient computation of solutions to complex linear equations
• Reducing computational costs in iterative algorithms
• Balancing precision and performance in computation

Benefits

The benefits of this technology include:

• Faster computation of solutions
• Improved efficiency in iterative algorithms
• Cost-effective computing solutions

Potential Commercial Applications

The technology could be utilized in industries such as:

• Finance
• Engineering
• Data analysis

Possible Prior Art

One possible prior art could be the use of low precision formats in computational algorithms to optimize performance and reduce computational costs.

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.

What are the limitations of using low precision formats in computational algorithms?

The article does not discuss the potential limitations or drawbacks of using low precision formats in computational algorithms.

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.