Radial Transform Radial Grid Trefethen Error (Log10) ------------------------ -------------------------- ----------- --------------- HandyModRTransform GaussChebyshev 2 -8.96559 HandyModRTransform FejerFirst 2 -8.94564 HandyModRTransform GaussLegendre 2 -8.93547 BeckeRTransform FejerSecond 1 -8.93038 HandyRTransform FejerSecond 1 -8.93038 HandyRTransform GaussChebyshevLobatto 1 -8.93004 BeckeRTransform GaussChebyshevLobatto 1 -8.93004 BeckeRTransform GaussChebyshevType2 1 -8.93 HandyRTransform GaussChebyshevType2 1 -8.93 HandyModRTransform GaussChebyshevType2 1 -8.9299 HandyModRTransform FejerSecond 1 -8.92984 BeckeRTransform GaussChebyshevType2 0 -8.92981 HandyRTransform GaussChebyshevType2 0 -8.92981 HandyModRTransform GaussLegendre 1 -8.92977 HandyRTransform FejerSecond 0 -8.92977 BeckeRTransform FejerSecond 0 -8.92977 BeckeRTransform GaussLegendre 0 -8.92976 BeckeRTransform FejerFirst 0 -8.92974 HandyRTransform FejerFirst 0 -8.92974 HandyRTransform GaussChebyshevLobatto 0 -8.92973 HandyRTransform GaussChebyshev 0 -8.92973 BeckeRTransform GaussChebyshev 0 -8.92973 BeckeRTransform GaussChebyshevLobatto 0 -8.92973 BeckeRTransform ClenshawCurtis 1 -8.92973 HandyRTransform ClenshawCurtis 1 -8.92973 HandyModRTransform FejerSecond 0 -8.92972 BeckeRTransform FejerFirst 1 -8.92972 HandyRTransform FejerFirst 1 -8.92972 HandyModRTransform GaussChebyshevLobatto 0 -8.92971 BeckeRTransform GaussChebyshev 1 -8.92971 HandyRTransform GaussChebyshev 1 -8.92971 HandyModRTransform GaussChebyshevType2 0 -8.92971 HandyModRTransform GaussChebyshevLobatto 1 -8.9297 BeckeRTransform GaussLegendre 1 -8.9297 HandyRTransform GaussLegendre 1 -8.9297 HandyModRTransform ClenshawCurtis 0 -8.9297 BeckeRTransform ClenshawCurtis 0 -8.92969 HandyRTransform ClenshawCurtis 0 -8.92969 HandyModRTransform FejerFirst 1 -8.92967 HandyModRTransform GaussLegendre 0 -8.92966 HandyModRTransform FejerFirst 0 -8.92966 HandyModRTransform GaussChebyshev 0 -8.92965 HandyModRTransform GaussChebyshev 1 -8.92965 HandyModRTransform ClenshawCurtis 1 -8.92963 HandyModRTransform ClenshawCurtis 2 -8.92046 BeckeRTransform GaussLegendre 2 -8.90992 HandyRTransform GaussLegendre 2 -8.90992 HandyRTransform ClenshawCurtis 2 -8.87921 BeckeRTransform ClenshawCurtis 2 -8.87921 HandyModRTransform GaussChebyshevType2 2 -8.87859 HandyModRTransform GaussChebyshevLobatto 2 -8.87852 HandyModRTransform FejerSecond 2 -8.87816 BeckeRTransform FejerFirst 2 -8.83079 HandyRTransform FejerFirst 2 -8.83079 BeckeRTransform GaussChebyshev 2 -8.82346 HandyRTransform GaussChebyshev 2 -8.82346 HandyRTransform GaussChebyshevType2 2 -8.81842 BeckeRTransform GaussChebyshevType2 2 -8.81842 HandyRTransform GaussChebyshevLobatto 2 -8.8118 BeckeRTransform GaussChebyshevLobatto 2 -8.8118 HandyRTransform FejerSecond 2 -8.77235 BeckeRTransform FejerSecond 2 -8.77235 KnowlesRTransform GaussLegendre 0 -8.7007 KnowlesRTransform FejerFirst 0 -8.69107 KnowlesRTransform ClenshawCurtis 0 -8.64118 KnowlesRTransform GaussChebyshev 0 -8.62135 KnowlesRTransform FejerFirst 1 -8.60352 KnowlesRTransform FejerSecond 0 -8.60319 KnowlesRTransform GaussChebyshevType2 0 -8.5867 KnowlesRTransform GaussChebyshevLobatto 0 -8.58549 KnowlesRTransform GaussLegendre 1 -8.5821 KnowlesRTransform ClenshawCurtis 1 -8.57373 KnowlesRTransform GaussChebyshev 1 -8.56657 KnowlesRTransform GaussChebyshevType2 1 -8.55144 KnowlesRTransform GaussChebyshevLobatto 1 -8.55139 KnowlesRTransform FejerSecond 1 -8.45612 HandyModRTransform MidPoint 0 -8.4146 KnowlesRTransform FejerFirst 2 -8.28187 KnowlesRTransform GaussChebyshev 2 -8.20808 KnowlesRTransform GaussLegendre 2 -8.2018 KnowlesRTransform ClenshawCurtis 2 -8.20177 HandyRTransform MidPoint 0 -8.18971 BeckeRTransform MidPoint 0 -8.18971 KnowlesRTransform GaussChebyshevType2 2 -8.1168 PowerRTransform GaussLaguerre 0 -8.10946 KnowlesRTransform GaussChebyshevLobatto 2 -8.10916 HandyModRTransform Trapezoidal 0 -8.10004 KnowlesRTransform FejerSecond 2 -7.87387 BeckeRTransform Trapezoidal 0 -7.85049 HandyRTransform Trapezoidal 0 -7.85049 HandyModRTransform MidPoint 1 -7.5647 BeckeRTransform Simpson 0 -7.49207 HandyRTransform Simpson 0 -7.49207 HandyModRTransform Trapezoidal 1 -7.39483 BeckeRTransform MidPoint 1 -7.04517 HandyRTransform MidPoint 1 -7.04517 BeckeRTransform Trapezoidal 1 -6.88862 HandyRTransform Trapezoidal 1 -6.88862 KnowlesRTransform MidPoint 0 -6.81699 KnowlesRTransform TanhSinh 2 -6.66121 KnowlesRTransform Trapezoidal 0 -6.5782 KnowlesRTransform Simpson 0 -6.57563 HandyModRTransform RectangleRuleSineEndPoints 0 -6.31842 HandyRTransform Simpson 1 -6.28807 BeckeRTransform Simpson 1 -6.28807 KnowlesRTransform TanhSinh 1 -6.21555 KnowlesRTransform MidPoint 1 -6.17881 KnowlesRTransform Trapezoidal 1 -5.9852 HandyRTransform RectangleRuleSineEndPoints 0 -5.77859 BeckeRTransform RectangleRuleSineEndPoints 0 -5.77859 KnowlesRTransform Simpson 1 -5.53479 KnowlesRTransform TanhSinh 0 -5.50081 HandyModRTransform RectangleRuleSineEndPoints 1 -5.48546 HandyModRTransform TanhSinh 2 -5.42788 HandyRTransform TanhSinh 2 -5.39437 BeckeRTransform TanhSinh 2 -5.39437 KnowlesRTransform RectangleRuleSineEndPoints 0 -5.38446 HandyRTransform RectangleRuleSineEndPoints 1 -4.95032 BeckeRTransform RectangleRuleSineEndPoints 1 -4.95032 ExpRTransform GaussLaguerre 0 -4.86713 HandyRTransform TanhSinh 1 -4.86474 BeckeRTransform TanhSinh 1 -4.86474 HandyModRTransform TanhSinh 1 -4.70471 KnowlesRTransform RectangleRuleSineEndPoints 1 -4.6743 BeckeRTransform TanhSinh 0 -4.17916 HandyRTransform TanhSinh 0 -4.17916 HandyModRTransform TanhSinh 0 -4.05734 HandyModRTransform RectangleRuleSineEndPoints 2 -4.00569 HandyModRTransform Simpson 2 -3.89973 HandyModRTransform MidPoint 2 -3.86439 HandyModRTransform Trapezoidal 2 -3.75888 BeckeRTransform RectangleRuleSineEndPoints 2 -3.6462 HandyRTransform RectangleRuleSineEndPoints 2 -3.6462 BeckeRTransform Simpson 2 -3.53248 HandyRTransform Simpson 2 -3.53248 LinearFiniteRTransform GaussChebyshevType2 0 -3.44344 LinearFiniteRTransform GaussChebyshev 0 -3.43639 KnowlesRTransform RectangleRuleSineEndPoints 2 -3.42597 LinearInfiniteRTransform GaussLaguerre 0 -3.41269 LinearFiniteRTransform ClenshawCurtis 0 -3.40959 LinearFiniteRTransform GaussChebyshevLobatto 0 -3.4071 KnowlesRTransform Simpson 2 -3.35786 LinearFiniteRTransform GaussLegendre 0 -3.35549 HandyRTransform MidPoint 2 -3.33056 BeckeRTransform MidPoint 2 -3.33056 LinearFiniteRTransform FejerFirst 0 -3.25951 HandyRTransform Trapezoidal 2 -3.21834 BeckeRTransform Trapezoidal 2 -3.21834 KnowlesRTransform MidPoint 2 -3.20062 KnowlesRTransform Trapezoidal 2 -2.99582 LinearFiniteRTransform FejerSecond 0 -2.86586 LinearFiniteRTransform GaussLegendre 1 -2.82932 LinearFiniteRTransform GaussChebyshev 1 -2.80366 LinearFiniteRTransform GaussChebyshevLobatto 1 -2.78582 LinearFiniteRTransform GaussChebyshevType2 1 -2.75362 LinearFiniteRTransform ClenshawCurtis 1 -2.69172 LinearFiniteRTransform FejerFirst 1 -2.55465 LinearFiniteRTransform FejerSecond 1 -2.29245 LinearFiniteRTransform TanhSinh 0 -2.22366 LinearFiniteRTransform TanhSinh 1 -2.14382 LinearFiniteRTransform TanhSinh 2 -1.86873 LinearFiniteRTransform GaussChebyshev 2 -1.34349 LinearFiniteRTransform GaussChebyshevType2 2 -1.31569 LinearFiniteRTransform FejerFirst 2 -1.31097 LinearFiniteRTransform GaussChebyshevLobatto 2 -1.29044 LinearFiniteRTransform ClenshawCurtis 2 -1.28898 LinearFiniteRTransform FejerSecond 2 -1.14414 LinearFiniteRTransform GaussLegendre 2 -1.13567 LinearFiniteRTransform MidPoint 0 -0.812253 LinearFiniteRTransform MidPoint 1 -0.114604 LinearFiniteRTransform Simpson 0 -0.0557317 LinearFiniteRTransform RectangleRuleSineEndPoints 0 -0.0500672 LinearFiniteRTransform Trapezoidal 0 -0.0411639 LinearFiniteRTransform Simpson 1 -0.00471505 LinearFiniteRTransform RectangleRuleSineEndPoints 1 -0.00429548 LinearFiniteRTransform Trapezoidal 1 -0.0035225 LinearFiniteRTransform MidPoint 2 -6.90396e-05 LinearFiniteRTransform Trapezoidal 2 -8.68392e-07 LinearFiniteRTransform Simpson 2 -6.72822e-07 LinearFiniteRTransform RectangleRuleSineEndPoints 2 -1.80887e-07 MultiExpRTransform RectangleRuleSineEndPoints 2 0.30078 MultiExpRTransform RectangleRuleSineEndPoints 1 0.301002 MultiExpRTransform RectangleRuleSineEndPoints 0 0.301009 MultiExpRTransform MidPoint 0 0.301025 MultiExpRTransform MidPoint 1 0.301025 MultiExpRTransform GaussChebyshevType2 2 0.301027 MultiExpRTransform FejerSecond 2 0.301028 MultiExpRTransform GaussLegendre 2 0.301029 MultiExpRTransform GaussChebyshevType2 1 0.301029 MultiExpRTransform GaussChebyshevType2 0 0.30103 MultiExpRTransform FejerSecond 1 0.30103 MultiExpRTransform FejerSecond 0 0.30103 MultiExpRTransform GaussLegendre 1 0.30103 MultiExpRTransform TanhSinh 2 0.30103 MultiExpRTransform GaussLegendre 0 0.30103 MultiExpRTransform FejerFirst 0 0.30103 MultiExpRTransform FejerFirst 2 0.30103 MultiExpRTransform FejerFirst 1 0.30103 MultiExpRTransform TanhSinh 1 0.30103 MultiExpRTransform GaussChebyshev 0 0.30103 MultiExpRTransform GaussChebyshev 1 0.30103 MultiExpRTransform TanhSinh 0 0.30103 MultiExpRTransform GaussChebyshev 2 0.301031 MultiExpRTransform MidPoint 2 0.301263