LSQR法在位场反演中的分析与评价

梁生贤, 王桥, 焦彦杰, 廖国忠, 郭境

Analysis and evaluation of the potential field inversion using LSQR method

Sheng-Xian LIANG, Qiao Wang, Yan-Jie JIAO, Guo-Zhong LIAO, Jing GUO

表1 LSQR算法

Table 1 Description of instruction in LSQR algorithm

初始化:
β₁μ₁=d, α₁ν₁=A^Tμ₁, ω₁=ν₁
m₀=0,

ρ_{1}^{*}

=α₁,

φ_{1}^{*}

=β₁

for i=1,2,3,…
β_i₊₁μ_i₊₁=Aν_i-α_iμ_i,
α_i₊₁ν_i₊₁=A^Tu_i₊₁-β_i₊₁ν_i,
ρ_i=

\sqrt[]{ρ_{i}^{* 2} + β_{i + 1}^{2}}

, c_i=

\frac{ρ_{i}^{*}}{ρ_{i}}

, s_i=

\frac{β_{i + 1}}{ρ_{i}}

,
θ_i₊₁=s_iα_i₊₁, φ_i=c_i

φ_{i}^{*}

ρ_{i + 1}^{*}

=-c_iα_i₊₁,

φ_{i + 1}^{*}

=s_i

φ_{i}^{*}

,
m_i₊₁=m_i+

\frac{φ_{i}}{ρ_{i}}

ω_i, ω_i₊₁=ν_i₊₁-

\frac{θ_{i + 1}}{ρ_{i}}

ω_i
是否达到迭代终止条件。