A double optimal descent algorithm for iteratively solving ill-posed linear inverse problems

Figures & data

Figure 1. For example 1 solved by the DODA with Krylov subspace, showing (a) residual, (b) $a_0$ and $\mathit{\beta }$ and (c) numerical error.

Figure 2. For example 1 under a large noise with $\mathit{\sigma }=0.05$, comparing numerical errors obtained by the DODA, DOS and GMRES.

Figure 3. For example 2 solved by the DODA with Krylov subspace, showing (a) residual, (b) $a_0$ and $\mathit{\beta }$ and (c) numerical error.

Figure 4. For example 2 solved by the DODA, GMRES, RRGMRES and OMVIA, comparing (a) residuals and (b) numerical errors.

Figure 5. For example 3 solved by the DODA with Krylov subspace, showing (a) residual, (b) $a_0$ and $\mathit{\beta }$ and (c) comparing numerical and exact solutions.

Figure 6. For example 3 solved by the DODA, DOS, GMRES, RRGMRES, OMVIA and OTVIA, comparing (a) residuals and (b) numerical errors.

Figure 7. For example 4 solved by the DODA with Krylov subspace, showing (a) residual, (b) $a_0$ and $\mathit{\beta }$ and (c) comparing numerical and exact solutions.

Figure 8. For example 4 solved by the DODA, DOS, GMRES, RRGMRES, OMVIA and OTVIA, comparing (a) residuals and (b) numerical errors.

Figure 9. For example 5 solved by the DODA and GMRES, showing (a) residuals, (b) $a_0$ and $\mathit{\beta }$, (c) comparing numerical and exact solutions and (d) numerical errors.