公开(公告)号：WO2010109359A2

公开(公告)日：2010-09-30

申请号：PCT/IB2010/050912

申请日：2010-03-03

Applicant: INTERNATIONAL BUSINESS MACHINES CORPORATION ,  BEKAS, Konstantinos ,  CURIONI, Alessandro

Inventor： BEKAS, Konstantinos ,  CURIONI, Alessandro

IPC: G06F17/12

CPC classification number: G06F17/12 ,  G06F17/16

Abstract: Apparatus and computer programs are provided for generating n high-precision data elements corresponding to an nx1 vector x satisfying Ax = b where A is a symmetric, positive- definite nxn matrix corresponding to nxn predefined high-precision data elements and b is an nx1 vector corresponding to n predefined high-precision data elements. The apparatus (1) comprises memory (3) for storing input data defining the data elements of matrix A and of vector b, and control logic (2). In a first processing step (a), the control logic (2) implements a first iterative process for generating from the input data n low-precision data elements corresponding to an nx1 vector x 1 satisfying A 1 x 1 = b 1 . Here, A 1 is an nxn matrix corresponding to the nxn data elements of matrix A in low precision and bi is an nx1 vector corresponding to the nx1 data elements of vector b in low precision. The control logic (2) terminates the first iterative process on occurrence of a first convergence condition. In a step (b), the control logic converts the data elements of vector x 1 to high-precision data elements to obtain a current solution vector x. In a step (c), control logic (2) implements a second iterative process for generating n low-precision data elements corresponding to an nxl correction vector dependent on the difference between the vector b and the vector product Ax. The control logic (2) terminates the second iterative process on occurrence of a second convergence condition. In a step (d), control logic (2) produces from the n low-precision data elements of the correction vector respective high-precision data elements of an nx1 update vector u, and then, in a step (e), updates the data elements of the current solution vector x such that x = x + u. The control logic (2) performs steps (c) to (e) until occurrence of a third convergence condition.

Abstract translation: 提供装置和计算机程序用于产生对应于满足Ax = b的nx1向量x的n个高精度数据元素，其中A是对应于nxn个预定义的高精度数据元素的对称正定nxn矩阵，b是nx1向量 对应于n个预定义的高精度数据元素。 装置（1）包括用于存储定义矩阵A和向量b的数据元素的输入数据的存储器（3）和控制逻辑（2）。 在第一处理步骤（a）中，控制逻辑（2）执行第一迭代处理，用于从输入数据生成与满足A1x1 = b1的nx1向量x1相对应的低精度数据元素。 这里，A1是以低精度对应于矩阵A的n×n个数据元素的n×n矩阵，bi是以低精度对应于向量b的n×1个数据元素的n×1向量。 控制逻辑（2）在出现第一收敛条件时终止第一迭代处理。 在步骤（b）中，控制逻辑将矢量x1的数据元素转换为高精度数据元素，以获得当前的解向量x。 在步骤（c）中，控制逻辑（2）执行第二迭代处理，用于根据向量b和向量积Ax之间的差产生对应于nxl校正向量的n个低精度数据元素。 控制逻辑（2）在发生第二收敛条件时终止第二迭代处理。 在步骤（d）中，控制逻辑（2）从校正矢量的n个低精度数据元素产生n×1更新向量u的相应高精度数据元素，然后在步骤（e）中更新 当前解向量x的数据元素使得x = x + u。 控制逻辑（2）执行步骤（c）至（e），直到发生第三收敛条件。

公开(公告)号：WO2010109359A3

公开(公告)日：2011-06-30

申请号：PCT/IB2010050912

申请日：2010-03-03

Applicant: IBM ,  BEKAS KONSTANTINOS ,  CURIONI ALESSANDRO

Inventor： BEKAS KONSTANTINOS ,  CURIONI ALESSANDRO

IPC: G06F17/12

CPC classification number: G06F17/12 ,  G06F17/16

Abstract: Apparatus and computer programs are provided for generating n high-precision data elements corresponding to an nx1 vector x satisfying Ax = b where A is a symmetric, positive- definite nxn matrix corresponding to nxn predefined high-precision data elements and b is an nx1 vector corresponding to n predefined high-precision data elements. The apparatus (1) comprises memory (3) for storing input data defining the data elements of matrix A and of vector b, and control logic (2). In a first processing step (a), the control logic (2) implements a first iterative process for generating from the input data n low-precision data elements corresponding to an nx1 vector x1 satisfying A1x1 = b1. Here, A1 is an nxn matrix corresponding to the nxn data elements of matrix A in low precision and bi is an nx1 vector corresponding to the nx1 data elements of vector b in low precision. The control logic (2) terminates the first iterative process on occurrence of a first convergence condition. In a step (b), the control logic converts the data elements of vector x1 to high-precision data elements to obtain a current solution vector x. In a step (c), control logic (2) implements a second iterative process for generating n low-precision data elements corresponding to an nxl correction vector dependent on the difference between the vector b and the vector product Ax. The control logic (2) terminates the second iterative process on occurrence of a second convergence condition. In a step (d), control logic (2) produces from the n low-precision data elements of the correction vector respective high-precision data elements of an nx1 update vector u, and then, in a step (e), updates the data elements of the current solution vector x such that x = x + u. The control logic (2) performs steps (c) to (e) until occurrence of a third convergence condition.

Abstract translation: 提供装置和计算机程序用于产生对应于满足Ax = b的nx1向量x的n个高精度数据元素，其中A是对应于nxn个预定义的高精度数据元素的对称正定nxn矩阵，b是nx1向量 对应于n个预定义的高精度数据元素。 装置（1）包括用于存储定义矩阵A和向量b以及控制逻辑（2）的数据元素的输入数据的存储器（3）。 在第一处理步骤（a）中，控制逻辑（2）执行第一迭代处理，用于从输入数据生成与满足A1x1 = b1的nx1向量x1相对应的低精度数据元素。 这里，A1是与精度较低的矩阵A的n×n个数据元素相对应的n×n矩阵，bi是与向量b的n×1个数据元素相对应的n×1向量，精度低。 控制逻辑（2）在出现第一收敛条件时终止第一迭代过程。 在步骤（b）中，控制逻辑将矢量x1的数据元素转换为高精度数据元素，以获得当前解向量x。 在步骤（c）中，控制逻辑（2）执行第二迭代处理，用于根据向量b和向量积Ax之间的差产生对应于nxl校正向量的n个低精度数据元素。 控制逻辑（2）在发生第二收敛条件时终止第二迭代处理。 在步骤（d）中，控制逻辑（2）从校正矢量的n个低精度数据元素产生n×1更新向量u的各个高精度数据元素，然后在步骤（e）中更新 当前解向量x的数据元素使得x = x + u。 控制逻辑（2）执行步骤（c）至（e），直到出现第三收敛条件。