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series_by_leastsquare

  

construct the least squares best fit linear subspace of a linear space of series

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

series_by_leastsquare(FS, conditions)

Parameters

FS

-

FPSstruct data structure (see Slode[FPseries])

conditions

-

set of linear conditions for the coefficients of the series

Description

• 

The series_by_leastsquare command determines from the given formal power series a series whose coefficients best satisfy the given linear conditions in the least squares sense and returns the result in form of an FPSstruct data structure.

• 

This command can be used in conjunction with Slode[FPseries] or Slode[FTseries] to construct a least-squares best fit power series solution for a linear ODE with respect to a system of linear constraint equations for some coefficients of the series solution. After constructing a formal series solution FS via Slode[FTseries] or Slode[FPseries], use the series_by_leastsquare command function with the result FS and the linear system as arguments.

Examples

withSlode:

ode1x1yx+x21diffyx,x=0

ode1x1yx+x21ⅆⅆxyx=0

(1)

sys1v850=v10,v10v38+v82=64,v3+v84=13

sys150v8=v10,v3+4v8=13,v108v3+2v8=64

(2)

fps1FPseriesode1,yx,vn:

series_by_leastsquarefps1,sys1

FPSstruct21202133924712120213x392471+2120213x23924712120213x3392471+2120213x43924712120213x5392471+2120213x63924712120213x7392471+2120213x83924712120213x9392471+2120213x10392471+n=11vnxn,nvn1+nvn

(3)

ode2x1yx+x21diffyx,x,x,x=0

ode2x1yx+x21ⅆ3ⅆx3yx=0

(4)

fps2FPseriesode2,yx,sn:

sys273s0+720s6=80,s0+s1+s2=3,s4+s6=7720,2s1s4=2,s1s2=0

sys273s0+720s6=80,s1s2=0,2s1s4=2,s4+s6=7720,s0+s1+s2=3

(5)

series_by_leastsquarefps2,sys2

FPSstruct1+x+x2x36x560+7x6720+n=7snxn,n33n2+2nsn+n36n2+11n6sn1+sn3

(6)

See Also

Slode

Slode[FPseries]

Slode[FTseries]