Letter from Rohedi Laboratory (Laboratory of New Science)
Dear All,
I interest to investigate the validity of output symbolic software especially for calculating the roots of polynomials . Now, I have been developing a new method for the purpose. The method can create analytical formulation for n order polynomials,
To show the performance of the method, firstly, I present the comparison the first root of the following polynomial to the matlab result.
From ROHEDI Laboratory
>>polinomn([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,500,51,52,53,
54,55,56,57,58,59,600,61,62,63,64,65,66,67,68,69,700,71,72,73,74,75,76,77,78,79,
800,81,82,83,84,85,86,87,88,89,900,91,92,93,94,95,96,97,98,99,1000,101,102,103,
104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,
124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,
144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,
164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,
184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,
204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,
224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,
244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,
264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,
284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,
304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,
324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,
344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,
364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,
384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,
404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,
424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,
444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,
464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,
484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,
504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,
524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,
544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,
564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,
584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,
604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,
624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,
644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,
664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,
684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,
704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,
724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,
744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,
764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,
784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,
804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,
824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,
844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,
864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,
884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,
904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,
924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,
944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,
964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,
984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,
1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,
1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,
1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,
1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061])
The first root of 1060 order polynomial above is
The root of matlab = 0.90967612057974 + 0.65233483663790i
with remainder = -5.386242315198940e+040 +3.112117014950832e+040i
matlab time consuming = 28.711 s.
myroot= -0.99461160642852 + 0.10321236597345i
with remainder = 9.436007530894131e-010 -5.946915848653589e-009i
my time consuming = 3.725 s.
My formula not only very accurate but also requires least of time consuming.
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