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WIP #83 - Matrix power via square decomposition #84

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WIP #83 - Matrix power via square decomposition #84

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@schillic schillic commented Jan 27, 2020 •
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Closes #83.

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This idea did not help much: there is almost no difference. Even the exact case is handled exactly in master.

Definitions

julia> B = IntervalMatrix([2.0±0 0.0±0; 0.0±0 3.0±0])
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
 [2, 2]  [0, 0]
 [0, 0]  [3, 3]

julia> C = [2.0 0.0; 0.0 3.0]
2×2 Array{Float64,2}:
 2.0  0.0
 0.0  3.0

julia> D = IntervalMatrix([2.0±0.1 0.0±0.1; 0.0±0.1 3.0±0.1])
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
  [1.89999, 2.10001]    [-0.100001, 0.100001]
 [-0.100001, 0.100001]   [2.89999, 3.10001]

This branch

julia> all(mid(B^k) == C^k for k in 1:20)
true

julia> B^20
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
     [1.04857e+06, 1.04858e+06]  [0, 0]                        
 [0, 0]                              [3.48678e+09, 3.48679e+09]

julia> D^20
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
 [-6.62849e+07, 7.20312e+07]  [-7.01882e+08, 7.01882e+08]
 [-7.01882e+08, 7.01882e+08]   [1.58595e+09, 7.09085e+09]

julia> B^16
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
 [65536, 65536]  [0, 0]                        
         [0, 0]      [4.30467e+07, 4.30468e+07]

julia> D^16
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
 [-664454, 874628]                          [-7.49338e+06, 7.49338e+06]
               [-7.49338e+06, 7.49338e+06]   [2.32098e+07, 7.58084e+07]

master

julia> all(mid(B^k) == C^k for k in 1:20)
true

julia> B^20
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
     [1.04857e+06, 1.04858e+06]  [0, 0]                        
 [0, 0]                              [3.48678e+09, 3.48679e+09]

julia> D^20
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
 [-6.78684e+07, 7.20312e+07]  [-7.01882e+08, 7.01882e+08]
 [-7.01882e+08, 7.01882e+08]   [1.5767e+09, 7.09085e+09] 

julia> B^16
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
 [65536, 65536]  [0, 0]                        
         [0, 0]      [4.30467e+07, 4.30468e+07]

julia> D^16
2×2 IntervalMatrix{Float64,Interval{Float64},Array{Interval{Float64},2}}:
 [-664454, 874628]                          [-7.49338e+06, 7.49338e+06]
               [-7.49338e+06, 7.49338e+06]   [2.32098e+07, 7.58084e+07]

@schillic schillic force-pushed the schillic/83 branch 3 times, most recently from c50de31 to c7d8d42 Compare January 27, 2020 16:11
@schillic schillic changed the title WIP #83 - Matrix power #83 - Matrix power Jan 27, 2020
@schillic schillic changed the title #83 - Matrix power #83 - Matrix power via square decomposition Feb 11, 2020
@schillic schillic changed the title #83 - Matrix power via square decomposition WIP #83 - Matrix power via square decomposition Feb 11, 2020
@schillic schillic marked this pull request as draft September 15, 2021 04:02
@schillic schillic closed this May 26, 2023
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Matrix power via square decomposition
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