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Student[NumericalAnalysis]

  

ForwardSubstitution

  

solve A.x = b where A is a lower-triangular matrix

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ForwardSubstitution(A, b)

ForwardSubstitution(A)

Parameters

A

-

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

b

-

(optional) Vector; a vector of length n

Description

• 

The ForwardSubstitution command returns a solution to the equation A.x=b, where A is a lower-triangular matrix, using the forward substitution algorithm.

Examples

withStudent[NumericalAnalysis]:

AMatrix1.1,4.9,7.7,4.4,7.5,8.1,2.7,8,10

A:=1.14.97.74.47.58.12.7810

(1)

bVector3.4,5.4,3.3

b:=3.45.43.3

(2)

Lower,UpperMatrixDecompositionA,method=LU,output='L','U'

Lower,Upper:=1004.000000000102.4545454550.33283245701,1.14.97.7012.1000000022.70000000001.344703226

(3)

cForwardSubstitutionLower,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[NumericalAnalysis]

Student[NumericalAnalysis][BackSubstitution]

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][IterativeApproximate]

Student[NumericalAnalysis][IterativeFormula]

Student[NumericalAnalysis][LinearSolve]

Student[NumericalAnalysis][MatrixDecomposition]

 


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