spaugment

---

构造最小二乘增广方程组

函数库: TyMath

语法

S = spaugment(A,c)
S = spaugment(A)

说明

S = spaugment(A,c) 创建对称不定稀疏方阵 S = [c*I A; A' 0]。矩阵 S 与最小二乘问题有关：

min norm(b - A*x)

by

r = b - A*x
S * [r/c; x] = [b; 0]

获取残差缩放因子 c 的最优值，往往涉及计算成本非常昂贵的调用： minimum(svd(A)) 和 norm(r)。

S = spaugment(A)（不带 c 的指定值）使用 maximum(abs, A)/1000。

示例

构造最小二乘增广方程组

using TyMath
spaugment(magic(3))

ans = 6×6 SparseMatrixCSC{Float64, Int64} with 21 stored entries:
 0.009   ⋅      ⋅     8.0  1.0  6.0
  ⋅     0.009   ⋅     3.0  5.0  7.0
  ⋅      ⋅     0.009  4.0  9.0  2.0
 8.0    3.0    4.0     ⋅    ⋅    ⋅
 1.0    5.0    9.0     ⋅    ⋅    ⋅
 6.0    7.0    2.0     ⋅    ⋅    ⋅

spaugment(magic(3),4)

ans = 6×6 SparseMatrixCSC{Float64, Int64} with 21 stored entries:
 4.0   ⋅    ⋅   8.0  1.0  6.0
  ⋅   4.0   ⋅   3.0  5.0  7.0
  ⋅    ⋅   4.0  4.0  9.0  2.0
 8.0  3.0  4.0   ⋅    ⋅    ⋅
 1.0  5.0  9.0   ⋅    ⋅    ⋅
 6.0  7.0  2.0   ⋅    ⋅    ⋅