diff options
Diffstat (limited to 'homeworks/hw-2.org')
| -rw-r--r-- | homeworks/hw-2.org | 80 |
1 files changed, 11 insertions, 69 deletions
diff --git a/homeworks/hw-2.org b/homeworks/hw-2.org index 9dad2d3..29502d7 100644 --- a/homeworks/hw-2.org +++ b/homeworks/hw-2.org @@ -45,7 +45,6 @@ Computing $\epsilon_{\text{mac}}$ for single precision numbers | 1.0 | 4.7683716e-07 | 4.7683716e-07 | | 1.0 | 2.3841858e-07 | 2.3841858e-07 | | 1.0 | 1.1920929e-07 | 1.1920929e-07 | -| 1.0 | 5.9604645e-08 | 0.0 | (with many rows truncated) @@ -54,14 +53,14 @@ Computing $\epsilon_{\text{mac}}$ for single precision numbers | 1.0 | 0.25 | 0.25 | | 1.0 | 0.125 | 0.125 | | 1.0 | 0.0625 | 0.0625 | +| 1.0 | 0.03125 | 0.03125 | | 1.0 | 1.9073486e-06 | 1.9073486e-06 | | 1.0 | 9.536743e-07 | 9.536743e-07 | | 1.0 | 4.7683716e-07 | 4.7683716e-07 | | 1.0 | 2.3841858e-07 | 2.3841858e-07 | | 1.0 | 1.1920929e-07 | 1.1920929e-07 | -| 1.0 | 5.9604645e-08 | 0.0 | -$\epsilon_{\text{mac}}$ \approx 5.9604 \cdot 10^{-8} +$\epsilon_{\text{mac single precision}}$ \approx 1.192(10^-7) * Question Two Computing $\epsilon_{\text{mac}}$ for double precision numbers: @@ -75,62 +74,6 @@ Computing $\epsilon_{\text{mac}}$ for double precision numbers: :domain-values domain-values))) #+END_SRC -#+RESULTS: -| a | h | err | -| 1.0d0 | 0.5d0 | 0.5d0 | -| 1.0d0 | 0.25d0 | 0.25d0 | -| 1.0d0 | 0.125d0 | 0.125d0 | -| 1.0d0 | 0.0625d0 | 0.0625d0 | -| 1.0d0 | 0.03125d0 | 0.03125d0 | -| 1.0d0 | 0.015625d0 | 0.015625d0 | -| 1.0d0 | 0.0078125d0 | 0.0078125d0 | -| 1.0d0 | 0.00390625d0 | 0.00390625d0 | -| 1.0d0 | 0.001953125d0 | 0.001953125d0 | -| 1.0d0 | 9.765625d-4 | 9.765625d-4 | -| 1.0d0 | 4.8828125d-4 | 4.8828125d-4 | -| 1.0d0 | 2.44140625d-4 | 2.44140625d-4 | -| 1.0d0 | 1.220703125d-4 | 1.220703125d-4 | -| 1.0d0 | 6.103515625d-5 | 6.103515625d-5 | -| 1.0d0 | 3.0517578125d-5 | 3.0517578125d-5 | -| 1.0d0 | 1.52587890625d-5 | 1.52587890625d-5 | -| 1.0d0 | 7.62939453125d-6 | 7.62939453125d-6 | -| 1.0d0 | 3.814697265625d-6 | 3.814697265625d-6 | -| 1.0d0 | 1.9073486328125d-6 | 1.9073486328125d-6 | -| 1.0d0 | 9.5367431640625d-7 | 9.5367431640625d-7 | -| 1.0d0 | 4.76837158203125d-7 | 4.76837158203125d-7 | -| 1.0d0 | 2.384185791015625d-7 | 2.384185791015625d-7 | -| 1.0d0 | 1.1920928955078125d-7 | 1.1920928955078125d-7 | -| 1.0d0 | 5.960464477539063d-8 | 5.960464477539063d-8 | -| 1.0d0 | 2.9802322387695313d-8 | 2.9802322387695313d-8 | -| 1.0d0 | 1.4901161193847656d-8 | 1.4901161193847656d-8 | -| 1.0d0 | 7.450580596923828d-9 | 7.450580596923828d-9 | -| 1.0d0 | 3.725290298461914d-9 | 3.725290298461914d-9 | -| 1.0d0 | 1.862645149230957d-9 | 1.862645149230957d-9 | -| 1.0d0 | 9.313225746154785d-10 | 9.313225746154785d-10 | -| 1.0d0 | 4.656612873077393d-10 | 4.656612873077393d-10 | -| 1.0d0 | 2.3283064365386963d-10 | 2.3283064365386963d-10 | -| 1.0d0 | 1.1641532182693481d-10 | 1.1641532182693481d-10 | -| 1.0d0 | 5.820766091346741d-11 | 5.820766091346741d-11 | -| 1.0d0 | 2.9103830456733704d-11 | 2.9103830456733704d-11 | -| 1.0d0 | 1.4551915228366852d-11 | 1.4551915228366852d-11 | -| 1.0d0 | 7.275957614183426d-12 | 7.275957614183426d-12 | -| 1.0d0 | 3.637978807091713d-12 | 3.637978807091713d-12 | -| 1.0d0 | 1.8189894035458565d-12 | 1.8189894035458565d-12 | -| 1.0d0 | 9.094947017729282d-13 | 9.094947017729282d-13 | -| 1.0d0 | 4.547473508864641d-13 | 4.547473508864641d-13 | -| 1.0d0 | 2.2737367544323206d-13 | 2.2737367544323206d-13 | -| 1.0d0 | 1.1368683772161603d-13 | 1.1368683772161603d-13 | -| 1.0d0 | 5.684341886080802d-14 | 5.684341886080802d-14 | -| 1.0d0 | 2.842170943040401d-14 | 2.842170943040401d-14 | -| 1.0d0 | 1.4210854715202004d-14 | 1.4210854715202004d-14 | -| 1.0d0 | 7.105427357601002d-15 | 7.105427357601002d-15 | -| 1.0d0 | 3.552713678800501d-15 | 3.552713678800501d-15 | -| 1.0d0 | 1.7763568394002505d-15 | 1.7763568394002505d-15 | -| 1.0d0 | 8.881784197001252d-16 | 8.881784197001252d-16 | -| 1.0d0 | 4.440892098500626d-16 | 4.440892098500626d-16 | -| 1.0d0 | 2.220446049250313d-16 | 2.220446049250313d-16 | -| 1.0d0 | 1.1102230246251565d-16 | 0.0d0 | - (with many rows truncated) | a | h | err | | 1.0d0 | 0.5d0 | 0.5d0 | @@ -148,9 +91,8 @@ Computing $\epsilon_{\text{mac}}$ for double precision numbers: | 1.0d0 | 8.881784197001252d-16 | 8.881784197001252d-16 | | 1.0d0 | 4.440892098500626d-16 | 4.440892098500626d-16 | | 1.0d0 | 2.220446049250313d-16 | 2.220446049250313d-16 | -| 1.0d0 | 1.1102230246251565d-16 | 0.0d0 | -Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16} +Thus, $\epsilon_{\text{mac double precision}}$ \approx 2.220 \cdot 10^{-16} * Question Three - |v|_2 #+BEGIN_SRC lisp :session t @@ -204,9 +146,9 @@ Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16} * Question Six - ||v - u|| via |v|_{2} #+BEGIN_SRC lisp :session t - (let* ((vs '((1 1) (2 3) (4 5) (-1 2))) - (vs2 '((7 9) (2 2) (8 -1) (4 4))) - (2-norm (lizfcm.vector:p-norm 2))) + (let ((vs '((1 1) (2 3) (4 5) (-1 2))) + (vs2 '((7 9) (2 2) (8 -1) (4 4))) + (2-norm (lizfcm.vector:p-norm 2))) (lizfcm.utils:table (:headers '("v1" "v2" "2-norm-d") :domain-order (v1 v2) :domain-values (mapcar (lambda (v1 v2) @@ -225,9 +167,9 @@ Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16} * Question Seven - ||v - u|| via |v|_{1} #+BEGIN_SRC lisp :session t - (let* ((vs '((1 1) (2 3) (4 5) (-1 2))) - (vs2 '((7 9) (2 2) (8 -1) (4 4))) - (1-norm (lizfcm.vector:p-norm 1))) + (let ((vs '((1 1) (2 3) (4 5) (-1 2))) + (vs2 '((7 9) (2 2) (8 -1) (4 4))) + (1-norm (lizfcm.vector:p-norm 1))) (lizfcm.utils:table (:headers '("v1" "v2" "1-norm-d") :domain-order (v1 v2) :domain-values (mapcar (lambda (v1 v2) @@ -246,8 +188,8 @@ Thus, $\epsilon_{\text{mac}}$ \approx 1.1102 \cdot 10^{-16} * Question Eight - ||v - u|| via |v|_{\infty} #+BEGIN_SRC lisp :session t - (let* ((vs '((1 1) (2 3) (4 5) (-1 2))) - (vs2 '((7 9) (2 2) (8 -1) (4 4)))) + (let ((vs '((1 1) (2 3) (4 5) (-1 2))) + (vs2 '((7 9) (2 2) (8 -1) (4 4)))) (lizfcm.utils:table (:headers '("v1" "v2" "max-norm-d") :domain-order (v1 v2) :domain-values (mapcar (lambda (v1 v2) |