Iterasi 2

library(mosaicCalc)

## Loading required package: mosaic

## Registered S3 method overwritten by 'mosaic':
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##   fortify.SpatialPolygonsDataFrame ggplot2

## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.

## 
## Attaching package: 'mosaic'

## The following objects are masked from 'package:dplyr':
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##     count, do, tally

## The following object is masked from 'package:Matrix':
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## The following objects are masked from 'package:stats':
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##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var

## The following objects are masked from 'package:base':
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##     max, mean, min, prod, range, sample, sum

## Loading required package: mosaicCore

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## Attaching package: 'mosaicCore'

## The following objects are masked from 'package:dplyr':
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## The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
## which was just loaded, will retire in October 2023.
## Please refer to R-spatial evolution reports for details, especially
## https://r-spatial.org/r/2023/05/15/evolution4.html.
## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.
## The sp package is now running under evolution status 2
##      (status 2 uses the sf package in place of rgdal)

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## Attaching package: 'mosaicCalc'

## The following object is masked from 'package:stats':
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##     D

Untuk mempermudah proses iterasi, kita akan menggunakan bantuan R untuk melakukan komputasi. Langkah pertama yang perlu dilakukan adalah menyiapkan matriks AA, vektor bb, dan vektor xx (nilai taksiran awal).

 (A <- matrix(c(3,2,1,2,9,3,3,5,6), 3))

##      [,1] [,2] [,3]
## [1,]    3    2    3
## [2,]    2    9    5
## [3,]    1    3    6

Algoritma Iterasi Jacobi:

Masukkan matriks
A dan vektor B beserta ukurannya n.

Hitung invers matriks D, dimana nilai invernya merupakan matriks diagonal dari satu per diagonal utama matriks A.

Hitung matriks R, dimana R merupakan selisih matriks A dikurangi dengan matriks diagonal dengan entri dari diagonal utama matriks A.

Tetapkan vektor x estimasi. Tetapkan nilai toleransi maksimum yang dapat diterima.

Lakukan iterasi Hitung akar jumlah kuadrat dari vektor
xn+1 dan vektor xn. Jadikan nilai xn+1

sebagai nilai taksiran x untuk iterasi berikutnya. Hentikan proses iterasi jika telah memenuhi syarat.