Math Problem Statement

当线性方程组的右端项很小时, 如何避免pcg 求解出错

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Preconditioned Conjugate Gradient (PCG) Method
Numerical Stability
Matrix Condition Number
Scaling of Linear Systems

Formulas

Ax = b (Linear system of equations)
Condition number of a matrix
PCG algorithm steps

Theorems

Conjugate Gradient Method
Numerical Stability Theorem

Suitable Grade Level

Advanced undergraduate or graduate level (Numerical Analysis)

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