International Scholarly Research Notices

Research Article

On the Convergence of the Modified Riccati Equation

Table 1

Calculation burden of matrix operations.
Matrix operationCalculation burden
𝐴 ( 𝑛 × 𝑛 ) + 𝐵 ( 𝑛 × 𝑛 ) = 𝑆 symmetric ( 1 / 2 ) ( 𝑛 2 + 𝑛 )
𝑐 ⋅ 𝑆 ( 𝑛 × 𝑛 ) symmetric ( 1 / 2 ) ( 𝑛 2 + 𝑛 )
𝐴 ( 𝑛 × 𝑚 ) ⋅ 𝐵 ( 𝑚 × 𝑘 ) = 𝐶 ( 𝑛 × 𝑘 ) 2 𝑛 𝑚 𝑘 − 𝑛 𝑘
𝐴 ( 𝑛 × 𝑚 ) ⋅ 𝐵 ( 𝑚 × 𝑛 ) = 𝑆 symmetric 𝑛 2 𝑚 + 𝑛 𝑚 − ( 1 / 2 ) ( 𝑛 2 + 𝑛 )
[ 𝐴 ( 𝑛 × 𝑛 ) ] − 1 = 𝐵 ( 𝑛 × 𝑛 ) ( 1 / 6 ) ( 1 6 𝑛 3 − 3 𝑛 2 − 𝑛 )