论文标题
vandermonde型矩阵的双节性分解任意等级
Bidiagonal Decompositions of Vandermonde-Type Matrices of Arbitrary Rank
论文作者
论文摘要
我们提出了一种用于获取Vandermonde及相关矩阵（例如（Q-，H-）Bernstein-Vandermonde等相关矩阵的BIDIAGONAL分解的新的显式表达方式的方法。这些结果将非矩阵的现有表达式推广到任意等级的矩阵。对于上述类别的完全非负矩阵，可以有效地计算出新的分解，并在浮点算术中构成高度相对精度。反过来，矩阵计算（例如，特征值计算）也可以有效地执行并达到高相对精度。
We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for nonsingular matrices to matrices of arbitrary rank. For totally nonnegative matrices of the above classes, the new decompositions can be computed efficiently and to high relative accuracy componentwise in floating point arithmetic. In turn, matrix computations (e.g., eigenvalue computation) can also be performed efficiently and to high relative accuracy.
