solve A.x = b where A is an upper-triangular matrix - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Education : Student Package : Numerical Analysis : Computation : Student/NumericalAnalysis/BackSubstitution

Student[NumericalAnalysis][BackSubstitution] - solve A.x = b where A is an upper-triangular matrix

Calling Sequence

BackSubstitution(A, b)

BackSubstitution(A)

Parameters

A

-

Matrix; an upper-triangular nxn matrix or an augmented (A|b) nxm matrix where m=n+1

b

-

(optional) Vector; a vector of length n

Description

• 

The BackSubstitution command returns a solution to the equation A.x=b, where A is an upper-triangular matrix, using the back substitution algorithm.

Examples

withStudent[NumericalAnalysis]:

A:=Matrix1.1,4.9,7.7,4.4,7.5,8.1,2.7,8,10

A:=1.14.97.74.47.58.12.7810

(1)

b:=Vector3.4,5.4,3.3

b:=3.45.43.3

(2)

Lower,Upper:=MatrixDecompositionA,method=LU,output='L','U'

Lower,Upper:=1004.000000000102.4545454550.33283245701,1.14.97.7012.1000000022.70000000001.344703226

(3)

c:=ForwardSubstitutionLower,b

c:=3.48.200000002.316228400

(4)

BackSubstitutionUpper,c=LinearSolveA,b,method=LU

2.4093194912.5537490341.722482965=2.4093194912.5537490341.722482965

(5)

See Also

Student[LinearAlgebra][BackwardSubstitute], Student[NumericalAnalysis], Student[NumericalAnalysis][ComputationOverview], Student[NumericalAnalysis][ForwardSubstitution], Student[NumericalAnalysis][IterativeApproximate], Student[NumericalAnalysis][IterativeFormula], Student[NumericalAnalysis][LinearSolve], Student[NumericalAnalysis][MatrixDecomposition]


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam