“LU Decomposition”的概念、定义、习题解题方法及翻译-数学辞典

单词

LU Decomposition

释义

LU Decomposition

A procedure for decomposing an matrix into a product of a lower Triangular Matrix and an upper Triangular Matrix ,

(1)

Written explicitly for a

Matrix, the decomposition is

(2)

(3)

This gives three types of equations

	(4)
	(5)
	(6)

This gives

equations for

unknowns (the decomposition is not unique), and can be solved using Crout'sMethod. To solve the Matrix equation

(7)

first solve

for

. This can be done by forward substitution

			(8)
			(9)

for

, ...,

. Then solve

for

. This can be done by back substitution

			(10)
			(11)

for

, ...,

See also Cholesky Decomposition, QR Decomposition,Triangular Matrix

References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``LU Decomposition and Its Applications.'' §2.3 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 34-42, 1992.

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