QR分解针对的对象不再是方阵了,这在LU分解上更进一步了;不过其目的还是一样,希望能够分解出来三角矩阵,然后使用forward/backward substitution来求解方程组。 存在性定理说明了这样的分解一定存在。 计算方法1:Gram-Schmidt Process 把A看作是n个m维向量的话,相当于是要把这n个向量用一组正交基底表示(因为要求了 QA...
4. **经济型QR分解**:如果只需要\( R \)矩阵或\( Q \)矩阵的某些特性,可以使用更节省计算资源的方法。 QR分解是一种在数值线性代数中广泛使用的技术,它在理论和实际应用中都非常重要。
The mathematic problem must be solved by complexQR decompositionalgorithm. 这个数学题必须用复数QR分解 算法解答. 互联网 A fragile watermarking algorithm based on wavelet transform andQR decompositionwas _ proposed. 提出一种基于小波变换和QR分解 的图像脆弱水印方法. ...
QRDecomposition[m] 给出数值矩阵 m 的 QR 分解. 结果为列表 {q, r},其中 q 是酉矩阵,r 是上三角矩阵.
QR DecompositionAfactorization of a matrix M of size m-by-n into an orthonormal matrix Q of size m-byn and an upper triangular [...] bdti.com bdti.com QR分解将大小为m乘n的矩阵M分解成一个大小为 m乘n的标准正交矩阵Q和一个大小为n乘n的上三角 ...
Full QR Decomposition of Matrix Compute the full QR decomposition of a magic square test matrix by specifying two output arguments. A = magic(5); [Q,R] = qr(A) Q =5×5-0.5234 0.5058 0.6735 -0.1215 -0.0441 -0.7081 -0.6966 -0.0177 0.0815 -0.0800 -0.1231 0.1367 -0.3558 -0.6307 -0.6646...
LinearAlgebra QRDecomposition compute QR factorization of a Matrix Calling Sequence Parameters Description Examples Calling Sequence QRDecomposition( A , fs , out , c , options , outopts ) Parameters A - Matrix fs - (optional) equation of the form fullsp
The QR decomposition is unique. PropositionUnder the assumptions of the previous proposition, the QR decomposition is unique, that is, the matrices and satisfying the stated properties are unique. Proof Pre-multiplication by the Q factor An important fact that we have discussed in the previous proo...
QR分解,QR decomposition 1)QR decompositionQR分解 1.Parallel algorithm of QR decomposition of matrix in cluster system;机群系统中矩阵的并行QR分解算法 2.A fragile watermarking algorithm based on QR decomposition;利用QR分解的脆弱水印算法 3.Discriminant dimensionality reduction based on QR decomposition and...
2 Computing the QR decomposition 2.1 Using the Gram–Schmidt process 2.1.1 Example 2.1.2 Relation to RQ decomposition 2.2 Using Householder reflections 2.2.1 Example 2.3 Using Givens rotations 2.3.1 Example 3 Connection to a determinant or a product of eigenvalues 4 Column pivoting 5 ...