User:Zhenlige/RTT notes: Difference between revisions

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<math>\begin{bmatrix}\boldsymbol{D}\\ \boldsymbol{F}\end{bmatrix}=\begin{bmatrix}\boldsymbol{B}&\boldsymbol{0}\\ \boldsymbol{0}&\mathbf{E}\end{bmatrix}^{-1}\boldsymbol{O}^{-1}=\begin{bmatrix}\boldsymbol{B}^{-1}&\boldsymbol{0}\\ \boldsymbol{0}&\mathbf{E}\end{bmatrix}\boldsymbol{O}^{-1}</math>，<math>\boldsymbol{D}=\begin{bmatrix}\boldsymbol{B}^{-1}&\boldsymbol{0}\end{bmatrix}\boldsymbol{O}^{-1}</math>，<math>g(\vec{b})=\left|\boldsymbol{D}^\mathrm{T}\vec{b}\right|</math>，又<math>\begin{bmatrix}\boldsymbol{D}\\ \boldsymbol{F}\end{bmatrix}\begin{bmatrix}\boldsymbol{A}&\boldsymbol{C}\end{bmatrix}=\mathbf{E}</math>，<math>\boldsymbol{D}\begin{bmatrix}\boldsymbol{A}&\boldsymbol{C}\end{bmatrix}=\begin{bmatrix}\mathbf{E}&\boldsymbol{0}\end{bmatrix}</math>，<math>\boldsymbol{D}=\boldsymbol{A}^+</math>，得证。

== ~~''p''范数调律 ''p''~~-~~norm~~ tuning ==

== 范数优化调律 norm-optimized tuning ==

参考：[[Dave Keenan & Douglas Blumeyer's guide to RTT/All-interval tuning schemes]]

目标：最小化损害<math>\frac{|\overleftarrow{r}\vec{\mathrm{i}}|}{f(\vec{\mathrm{i}})}</math>的上界，其中<math>f</math>为范数函数。根据对偶范数定义，即最小化<math>\mathrm{dual}_f\left(\overleftarrow{r}^\mathrm{T}\right)</math>。

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 <math>\begin{bmatrix}\boldsymbol{D}\\ \boldsymbol{F}\end{bmatrix}=\begin{bmatrix}\boldsymbol{B}&\boldsymbol{0}\\ \boldsymbol{0}&\mathbf{E}\end{bmatrix}^{-1}\boldsymbol{O}^{-1}=\begin{bmatrix}\boldsymbol{B}^{-1}&\boldsymbol{0}\\ \boldsymbol{0}&\mathbf{E}\end{bmatrix}\boldsymbol{O}^{-1}</math>，<math>\boldsymbol{D}=\begin{bmatrix}\boldsymbol{B}^{-1}&\boldsymbol{0}\end{bmatrix}\boldsymbol{O}^{-1}</math>，<math>g(\vec{b})=\left|\boldsymbol{D}^\mathrm{T}\vec{b}\right|</math>，又<math>\begin{bmatrix}\boldsymbol{D}\\ \boldsymbol{F}\end{bmatrix}\begin{bmatrix}\boldsymbol{A}&\boldsymbol{C}\end{bmatrix}=\mathbf{E}</math>，<math>\boldsymbol{D}\begin{bmatrix}\boldsymbol{A}&\boldsymbol{C}\end{bmatrix}=\begin{bmatrix}\mathbf{E}&\boldsymbol{0}\end{bmatrix}</math>，<math>\boldsymbol{D}=\boldsymbol{A}^+</math>，得证。
-== ''p''范数调律 ''p''-norm tuning ==
+== 范数优化调律 norm-optimized tuning ==
+参考：[[Dave Keenan & Douglas Blumeyer's guide to RTT/All-interval tuning schemes]]
+目标：最小化损害<math>\frac{|\overleftarrow{r}\vec{\mathrm{i}}|}{f(\vec{\mathrm{i}})}</math>的上界，其中<math>f</math>为范数函数。根据对偶范数定义，即最小化<math>\mathrm{dual}_f\left(\overleftarrow{r}^\mathrm{T}\right)</math>。