Solve a test problem using manually selected rules

The problem Upload file:

Or select matrix and solution vector below.

Matrix baart deriv2 foxgood gravity heat κ = i_laplace phillips shaw spikes t_max = wing gauss σ = hilbert lotkin moler α = pascal prolate w =		Solution baart deriv2 example = foxgood gravity heat i_laplace example = phillips shaw spikes t_max = wing t₁ = t₂ = constant linear quadratic sinusoidal linear+sinusoidal step function
Problem size:

Additional smoothness:
Normalize problem

Noise level

Right hand side

Noise distribution:
normal
uniform
Poisson λ =
normal with outlier

Noise level:
relative absolute
actual noise level standard deviation

Correlation coefficient:

Matrix

Noise distribution:
normal
uniform

Noise level:
relative absolute
actual noise level standard deviation

Number of noise vectors:
Random seed:

Information about noise

	Upper bounds δ = η =
	These are relative absolute noise levels.
	Standard deviation σ = σ_η =
	These are relative absolute noise levels.
	No information about noise is known.

Parameter choice rules

Delta-rules

Unstable delta-rules
Discrepancy principle (D)	c =
Monotone error rule (ME)	c =
ME rule with post-estimation (MEe) γ =	c =
Adjusted monotone error rule (MEa)
Raus-Gfrerer rule (RG)	c =
Stable delta-rules
Balancing principle (BP)	c =
Rule R1 k =	c =
Rule R2(q=2, k=2, l=1/2)	c =
Rule R2(q=2, k=1, l=1/2)	c =
A priori parameter selection
A priori (Apri) α =

Heuristic rules

Quasioptimality criterion (Q)	κ	Nb
Hanke-Raus rule (HR)	κ	Nb
Regińska's rule (Reg) τ =	κ	Nb
Modified Regińska's rule (MReg)	κ	Nb
Hybrid rule (Hyb)
Brezinski-Rodriguez-Seatzu rule (BRS)	κ	Nb
Generalized cross-validation (GCV)	κ	Nb
Robust generalized cross-validation (RGCV) γ =	κ	Nb
Strong robust generalized cross-validation (SRGCV) γ =	κ	Nb
Modified generalized cross-validation (MGCV) c =	κ	Nb
Generalized maximum likelihood method (GML)	κ	Nb
Residual method (Res)	κ	Nb
HR monotone error rule (HRME)	κ	Nb
HR(1/4) rule	κ	Nb

Technical Parameter interval: α_M = α₀ = stepsize q =

Solution graph

If the number of runs is 1.

	ME c=1	RG c=1.2	Q Nb	HR κ Nb	Hyb	Optimal
Parameter	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6	3.37e-6
Error	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6	3.37e-6
Relative error	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6	3.37e-6
Error ratio	5.34	1.34	2.50	4.34	5.96
Quasi ratio	5.34	1.34	2.50	4.34	5.96
T₁(α_H)	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6
T₂(α_H)	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6
Link to solution	Link	Link	Link	Link	Link	Link

If the number of runs is >1.

Nr		ME c=1	RG c=1.2	Q Nb	HR κ Nb	Hyb	Optimal
1	Parameter	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6	3.37e-6
2	Parameter	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6	3.37e-6
3	Parameter	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6	3.37e-6
1	Error ratio	5.34	1.34	2.50	4.34	5.96	2.67e-4*
2	Error ratio	5.34	1.34	2.50	4.34	5.96	2.67e-4*
3	Error ratio	5.34	1.34	2.50	4.34	5.96	2.67e-4*
	Average error	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6	3.37e-6
	Avg rel error	5.34e-5	1.34e-6	2.50e-5	4.34e-10	5.96e-6	3.37e-6
	Avg error ratio	5.34	1.34	2.50	4.34	5.96
	Median error ratio	5.34	1.34	2.50	4.34	5.96
	Max error ratio	5.34	1.34	2.50	4.34	5.96
	Avg quasi ratio	5.34	1.34	2.50	4.34	5.96
	Max quasi ratio	5.34	1.34	2.50	4.34	5.96
1	Link to solution	Link	Link	Link	Link	Link	Link
2	Link to solution	Link	Link	Link	Link	Link	Link
3	Link to solution	Link	Link	Link	Link	Link	Link

*Absolute error