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keisanHigh-precision calculations for everyday life and work

2x2 Square Matrix, Real Symmetric, Newton's Method

Author: shiroeExecutions: 17

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This is a numerical diagonalization method for a 2x2 square matrix that is real and symmetric.
Since it is a 2x2 square matrix and a symmetric matrix, the process is simplified because the step of finding the “non-diagonal element with the largest absolute value” can be omitted.
Furthermore, converting the problem to linear expressions for `cos2θ` and `sin2θ` reduces the period, improving the efficiency of interval discovery and shortening the process using the bisection method.
The Newton approximation is applied within the reduced interval.
The precision has been set to 100 intervals per iteration, with an interval width of 0.1^15; for the Newton approximation, this has been reduced to 0.1^20.
Outputs the matrix elements after processing.
The rest is for reference.
a
  (Diagonal elements)
b
  (Off-diagonal elements) (assuming c = b)
d
  (Diagonal elements)
QAP(1,1)   (Diagonal elements)
QAP(1,2)   (Off-diagonal elements)
QAP(2,1)   (Off-diagonal elements)
QAP(2,2)   (Diagonal elements)
θ (Radians)
Value of cosθ 
Value of sinθ 
Value of tanθ 
2θ (Radians
Value of cos2θ 
Value of sin2θ 
Value of tan2θ 
The value of (θ/2π)*360   (Rounding down to the nearest whole number)
Digit display setting: 6 digits. Digit count can be changed. Real number calculation mode.
(Note: Check whether the calculation result ends with “E-??”)

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