lapack - LAPACK中的DGESVD实现了哪种算法？

Question

我很好奇用于在 MATLAB 中计算 SVD 的 DGESVD 函数。据我从 Gene H. Golub 和 Charles F. Van Loan 的“矩阵计算”中可以看出，使用了两种可能的双对角化方案 - 家庭双对角化和 R 对角化。但是，我无法从正在使用的 LAPACK 文档中确定。任何人有任何想法？

Answer 1

根据LAPACK User's Guide ，减少到双对角形式是由常规 DGEBRD 完成的，它使用 Householder 反射。

2.4.6“奇异值分解”:

The routine xGEBRD represents U1 and V1 in factored form as products of elementary reflectors, as described in section 5.4.

5.4“正交或酉矩阵的表示”:

A real orthogonal or complex unitary matrix (usually denoted Q) is often represented in LAPACK as a product of elementary reflectors -- also referred to as elementary Householder matrices