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Computer assisted Fourier analysis in sequence spaces of varying regularity
J.-P. Lessard and J.D. Mireles James
SIAM Journal on Mathematical Analysis, 49(1), 530–561, 2017
PDF doi:10.1137/16m1056006 Publication [30]
Files
Codes and data accompanying the paper, reproducing the computer-assisted proofs it reports.
codes/ — 72 files (8.6 MB)
- Analytic_proofs/ck_analytic_paperCode1.m (1.5 KB)
- Analytic_proofs/cubic_FFT.m (361 B)
- Analytic_proofs/ellNuOne_MatrixNorm_intval.m (753 B)
- Analytic_proofs/ellOneNorm_intval.m (392 B)
- Analytic_proofs/ex1_analyticBump_branch1.mat (384 KB)
- Analytic_proofs/ex1_analyticBump_branch2.mat (379 KB)
- Analytic_proofs/ex1_analyticBump_branch3.mat (482 KB)
- Analytic_proofs/ex1_analyticBump_branch4.mat (501 KB)
- Analytic_proofs/ex1_analyticBump_branch5.mat (559 KB)
- Analytic_proofs/fft_data.mat (227 KB)
- Analytic_proofs/fisherEquilibriumAnalyticProof.m (1.8 KB)
- Analytic_proofs/fisherMapII_Differential_cos_intval.m (1.0 KB)
- Analytic_proofs/fisherMapII_cos_intval.m (136 B)
- Analytic_proofs/fisherStabilityAnalyticProof.m (4.9 KB)
- Analytic_proofs/int_c_analyticBump_ex1.m (320 B)
- Analytic_proofs/int_cubic_sumFFT.m (726 B)
- Analytic_proofs/int_quadratic_sumFFT.m (601 B)
- Analytic_proofs/int_radii_polynomial_analytic.m (1.1 KB)
- Analytic_proofs/kappaBounds.m (1.3 KB)
- Analytic_proofs/oneDcubic_sumFFT.m (375 B)
- Analytic_proofs/plot_equilibrium.m (421 B)
- Analytic_proofs/pt1_breakdown.mat (8.2 KB)
- Analytic_proofs/pt2_breakdown.mat (92 KB)
- Analytic_proofs/pt3_breakdown.mat (9.6 KB)
- Analytic_proofs/script_analytic_proof_ex1_th1.m (3.7 KB)
- Analytic_proofs/script_proof_analytic_th1.m (2.9 KB)
- Analytic_proofs/verifyfft.m (2.3 KB)
- Ck_proofs/ALPHA_1pt3_M_2000.mat (53 KB)
- Ck_proofs/ALPHA_1pt3_M_3000.mat (77 KB)
- Ck_proofs/ALPHA_1pt3_M_800.mat (23 KB)
- Ck_proofs/DF_Fisher.m (450 B)
- Ck_proofs/F_Fisher.m (309 B)
- Ck_proofs/c_analyticBump_ex1.m (174 B)
- Ck_proofs/c_continuous_non_Lipschitz_ex5.m (112 B)
- Ck_proofs/c_smooth_non_analytic_ex2.m (167 B)
- Ck_proofs/cubic_FFT.m (361 B)
- Ck_proofs/ex1_analyticBump_branch1.mat (384 KB)
- Ck_proofs/ex1_analyticBump_branch2.mat (379 KB)
- Ck_proofs/ex1_analyticBump_branch3.mat (482 KB)
- Ck_proofs/ex1_analyticBump_branch4.mat (501 KB)
- Ck_proofs/ex1_analyticBump_branch5.mat (559 KB)
- Ck_proofs/ex2_coexisting_pts_mu1000.mat (16 KB)
- Ck_proofs/ex2_coexisting_pts_mu3pt75.mat (8.5 KB)
- Ck_proofs/ex2_coexisting_pts_mu4pt5.mat (8.5 KB)
- Ck_proofs/ex2_smooth_non_analytic_branch1.mat (156 KB)
- Ck_proofs/ex2_smooth_non_analytic_branch2.mat (140 KB)
- Ck_proofs/ex2_smooth_non_analytic_branch3.mat (47 KB)
- Ck_proofs/ex5_continuous_non_Lipschitz_branch1.mat (516 KB)
- Ck_proofs/ex5_continuous_non_Lipschitz_branch2.mat (272 KB)
- Ck_proofs/ex5_continuous_non_Lipschitz_branch3.mat (572 KB)
- Ck_proofs/ex5_continuous_non_Lipschitz_branch4.mat (571 KB)
- Ck_proofs/ex5_continuous_non_Lipschitz_branch5.mat (515 KB)
- Ck_proofs/ex5_continuous_non_Lipschitz_branch6.mat (572 KB)
- Ck_proofs/fft_data.mat (227 KB)
- Ck_proofs/int_DF_Fisher.m (684 B)
- Ck_proofs/int_F_Fisher.m (136 B)
- Ck_proofs/int_c_analyticBump_ex1.m (320 B)
- Ck_proofs/int_c_continuous_non_Lipschitz_ex5.m (149 B)
- Ck_proofs/int_c_smooth_non_analytic_ex2.m (208 B)
- Ck_proofs/int_cubic_sumFFT.m (808 B)
- Ck_proofs/int_radii_polynomial.m (6.0 KB)
- Ck_proofs/newton_F_Fisher.m (575 B)
- Ck_proofs/plot_equilibrium.m (421 B)
- Ck_proofs/pt0_breakdown.mat (8.1 KB)
- Ck_proofs/script_breakdown.m (614 B)
- Ck_proofs/script_proof_ex1_th1.m (3.0 KB)
- Ck_proofs/script_proof_ex2_th1.m (1.3 KB)
- Ck_proofs/script_proof_ex2_th2.m (614 B)
- Ck_proofs/script_proof_ex2_th3.m (613 B)
- Ck_proofs/script_proof_ex2_th4.m (824 B)
- Ck_proofs/script_proof_ex5_th1.m (3.0 KB)
- Ck_proofs/verifyfft.m (2.3 KB)
The scripts are written in MATLAB; the rigorous parts require the interval arithmetic package INTLAB to be installed and started.