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Technique for solving linear equation systems with multiple right hand sides by KRYLOV subspace expansion

A system of linear equations, subspace technology, applied in the field of general computing, can solve problems such as exceeding the available time, implementing transformation time, etc., to achieve the effect of overall performance improvement

Inactive Publication Date: 2014-02-12
NVIDIA CORP
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

However, implementing the transformation is still very time-consuming
And, despite the reduction in execution time, in many applications this method still exceeds the available time

Method used

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  • Technique for solving linear equation systems with multiple right hand sides by KRYLOV subspace expansion
  • Technique for solving linear equation systems with multiple right hand sides by KRYLOV subspace expansion
  • Technique for solving linear equation systems with multiple right hand sides by KRYLOV subspace expansion

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Embodiment Construction

[0017] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without one or more of these specific details.

[0018] figure 1 is a block diagram illustrating a computer system 100 configured to implement one or more aspects of the present invention. As shown, computer system 100 includes, but is not limited to, a central processing unit (CPU) 102 and system memory 104 that communicate via an interconnection path that may include a memory bridge 105 . The memory bridge 105 may be, for example, a north bridge chip, connected to an I / O (input / output) bridge 107 via a bus or other communication path 106 (eg, a HyperTransport link). I / O bridge 107 , which may be, for example, a south bridge chip, receives user input from one or more user input devices 108 (eg, keyboard, mouse) and forwards the i...

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Abstract

One embodiment sets forth a method for solving linear equation systems that include the same matrix A coupled with multiple right-hand-side vectors. For each new right-hand-side vector, a solver expands an existing Krylov subspace based on the Krylov subspace and data associated with the previous right-hand-side vector. The solver then uses the expanded Krylov subspace to approximately solve the linear equation system for the new right-hand-side vector. By expanding the Krylov subspace for each new right-hand-side vector, the solver continually leverages the information from the preceding right-hand-side vectors. Advantageously, expanding the Krylov subspace is typically computationally quicker than prior art-techniques, such as creating a new Krylov subspace or transforming an existing Krylov subspace. Consequently, by implementing the disclosed techniques, the likelihood of exceeding time constraints associated with algorithms that include solving certain classes of linear equation systems may be decreased.

Description

[0001] Cross References to Related Applications [0002] This application claims priority to US Provisional Patent Application Serial No. 61 / 672,487, filed July 17, 2012, which is hereby incorporated by reference. technical field [0003] The present invention relates generally to general purpose computing, and, more particularly, to techniques for solving systems of linear equations with multiple right hand sides via Krylov subspace extensions. Background technique [0004] Systems of linear equations arise in many applications of scientific computing in a wide range of fields such as chemistry, structural analysis, physics, mathematics, etc. And solving such systems of linear equations is an important part of many algorithms used in these fields, such as chemical process simulation algorithms. It is well known that a system of linear equations can be expressed in matrix form as Ax=RHS. In general, elements included in a system of linear equations exhibit similarities ba...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/12
CPCG06F17/12
Inventor 罗伯特·斯特兹欧迪卡
Owner NVIDIA CORP
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