-4
我已方程Ax = b的有下列11×11個線性系統：求解線性方程組的病態系統LAPACK＆CO
A = {
{1.0000000000000000, 8.0000000000000000, 6.0000000000000000, 12.0000000000000000, 24.0000000000000000, 24.0000000000000000, 8.0000000000000000, 6.0000000000000000, 24.0000000000000000, 24.0000000000000000, 24.0000000000000000},
{4.5999999999999996, 41.8531411531233601, 33.0479488942856037, 87.8349057232554173, 149.3783917109033439, 195.3689938163366833, 121.0451669808013690, 48.8422484540841708, 223.6406089026404516, 851.8470736603384239, 269.3015780207464900},
{21.1599999999999966, 218.9606780479085160, 182.0278210198854936, 642.9142219510971472, 929.7459962556697519, 1590.3768227003254196, 1831.4915561762611560, 397.5942056750813549, 2083.9634145976574473, 30235.1432043200838962, 3021.8058301860087340},
{97.3359999999999701, 1145.5240206653393216, 1002.6076877338904296, 4705.8591727678940515, 5786.8317341801457587, 12946.2633183243797248, 27711.6501551604087581, 3236.5658295810949312, 19419.1186238102454809, 1073154.9275125553831458, 33907.3782725576675148},
{447.7455999999998539, 5992.9723163999815370, 5522.3546042079124163, 34444.8913989153879811, 36017.8173980603314703, 105387.4349242659372976, 419295.1650431178859435, 26346.8587310664843244, 180954.3130575636751018, 38090161.8577392920851707, 380471.2698060897528194},
{0.0000000000000000, 34.2801357124991952, 168.4702728821191613, 2101.6181209908259007, 1236.1435394200643714, 6631.0420254749351443, 38374.2674650820554234, 4069.0485156323466072, 28291.8793721561523853, 7044717.1197200166061521, 60211.4334496619121637},
{2059.6297599999993508, 31353.0895356311411888, 30417.0821226643129194, 252121.9823892920394428, 224178.4848274685500655, 857893.2134182706940919, 6344206.6583608603104949, 214473.3033545676735230, 1686197.1981563565786928, 1351958038.0734937191009521, 4269229.7229307144880295},
{0.0000000000000000, 179.3414198404317403, 927.9328280691040618, 15382.9524602928686363, 7693.8805767663707229, 53979.1670196200575447, 580627.4516345988959074, 33123.5797620395824197, 263633.8804078772664070, 250042569.2999326586723328, 675626.4184535464737564},
{0.0000000000000000, 938.2502198978935439, 5111.0461132262771571, 112596.6815912620077142, 47887.4794405465727323, 439410.6478194649680518, 8785268.3545934017747641, 269638.3520710353623144, 2456635.0642409822903574, 8874917956.1941699981689453, 7581135.8600852200761437},
{0.0000000000000000, 938.2502198978935439, 0.0000000000000000, 56298.3407956310038571, 23943.7397202732863661, 319571.3802323381532915, 8785268.3545934017747641, 0.0000000000000000, 269630.6777825467870571, 3293783983.7421655654907227, 1735440.7390556528698653},
{0.0000000000000000, 70.9608494071368625, 1546.2151390406352220, 34063.2210755480555235, 13279.8613116998949408, 129911.1650312914862297, 2657756.2850107550621033, 183537.2854802548536099, 1654054.3836708476301283, 5487391301.6329326629638672, 5049794.3807012736797333}
};
b = {1, 6.167551546217714, 39.66265463865314, 267.9960092725794, 1918.2310370808632, 137.49061855461255, 14662.396462231256, 1216.4598834815756, 11424.520672986631, 3808.17355766221, 6082.299417407878};
矩陣被清楚地病態，雖然正確的解決方案能夠以發現mathematica：
x = {0.0775277, 0.00771443, 0.087553, 0.0208838, 8.47931*1e-7, 0.00197285, 0.0000611365, 0.00187375, 0.000283606, 3.82771*1e-9, 0.000788588};
我現在想解決在C程序中使用這個和許多其他類似矩陣的系統。 我已經試過幾乎所有LAPACK函數求解線性方程系統，特別是：
- dgesv
- dsgesv
- dgels
- dgelss
- dgelsy
，但他們都給出了嚴重錯誤的結果。
在這一點上，我並不期望從編程的角度來看有任何錯字/錯誤，因爲嘗試使用條件良好的矩陣，我會得到正確的結果。 我想這是概念上的東西，也許我必須使用其他工具..有什麼我可以做的，以找到正確的解決方案與數學圖書館的一些例程？
在這種情況下發布的價值觀是完全沒有必要的，而不是你應該張貼你如何** **嘗試使用* LAPACK *來解決這個問題。另外，如果你知道結果是錯的，它必須是因爲你可以用不同的方法解決這個問題，你爲什麼要在[tag：c]中使用它？ –
你在問一個數學問題，而不是一個編程問題。 – kangshiyin