[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"$fkoz-tu1GwnlbNH3ocyQTVqcZSH8aiKECUGkEadt6IaQ":3},{"answer":4,"createTime":5,"id":6,"options":7,"origin":10,"question":16,"related":17,"source":23,"type":24},[],"2023-05-07 22:58:31",84480199,[8,9],"对","错",{"courseId":11,"courseImg":12,"courseName":13,"workId":14,"workName":15},"1000011058","https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fe897508696b95a312b0f5f065eec61e1.jpeg","高等工程数学","29064272","高等工程数学教程考试","若A是列满秩矩阵,则矛盾方程组Ax=b的最小二乘解x0满足AHAx0=AHb,且有唯一解x0",[18,25,35,44,54,63,72,81,86,91],{"answer":19,"createTime":5,"id":20,"options":21,"question":22,"source":23,"type":24},[],84480171,[8,9],"设\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fe09df43bf935eeea5e147c5e805e07f9.png\">对称,经Gauss顺序消去法一步后A变为\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fc1cb6c8f94169f46e6d9ed903f1dfe16.png\">其中\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F2964db61c68b5976c2d33393f2b955b2.png\">是\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fda8a0a59ce162768746b3b5c6598e99b.png\">阶矩阵,那么\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F2964db61c68b5976c2d33393f2b955b2.png\">仍为对称阵","v2",3,{"answer":26,"createTime":5,"id":27,"options":28,"question":33,"source":23,"type":34},[],84480174,[29,30,31,32],"若系数矩阵A实对称正定,且松弛因子\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F97f06191796f7fd55a89b77a33a911be.png\">,则SOR法收敛","若系数矩阵A严格对角占优,则SOR法收敛的充要条件是松弛因子\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F7e4f94936af664c9b98ab84fe745314b.png\">","J迭代法和G-S迭代法的敛散性无关联","选取的松弛因子不同,SOR迭代法的敛散性或收敛速度不同","下面说法正确的是",1,{"answer":36,"createTime":5,"id":37,"options":38,"question":43,"source":23,"type":34},[],84480176,[39,40,41,42],"共轭梯度法第k步迭代点是经过初始点由各步搜索方向p0,p1,…,pk-1张成的空间中的极小值点,因此具有某种"全局"最优性","不计舍入误差,共轭梯度法至多经n步便得线性方程组的解","最速下降法和共轭梯度法都是极小化方法","最速下降法的每一步的搜索方向为上一步迭代点的负梯度方向","下面说法正确的是( )",{"answer":45,"createTime":5,"id":46,"options":47,"question":52,"source":23,"type":53},[],84480177,[48,49,50,51],"6\u002F55(1,-6,1)T, 114\u002F552(-1,18,-1)T","114\u002F552(-1,18,-1)T, 6\u002F55(1,-6,1)T","6\u002F55(-1,6,-1)T, 114\u002F552(-1,18,-1)T","114\u002F552(-1,18,-1)T, 6\u002F55(-1,6,-1)T","用最速下降法和共轭梯度法求解方程组:\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fce2e0bb1c4a20d9fe8993ba479754c18.png\">选取(0,0,0)T作为初值,则第二步迭代的搜索方向分别为( )",0,{"answer":55,"createTime":5,"id":56,"options":57,"question":62,"source":23,"type":53},[],84480178,[58,59,60,61],"-5\u002F3","5\u002F3","7\u002F3","3","用列主元法解线性方程组:\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fa0da32f77ccc1255bc3e8b8d56571c53.png\">第二步消元的主元是( )",{"answer":64,"createTime":5,"id":65,"options":66,"question":71,"source":23,"type":53},[],84480187,[67,68,69,70],"x=AA+b","x=A+Ab","x=A+b","都不是","下列哪项是矛盾方程组Ax=b的极小范数最小二乘解( )",{"answer":73,"createTime":5,"id":74,"options":75,"question":80,"source":23,"type":34},[],84480188,[76,77,78,79],"不存在三角分解","不存在Doolittle分解","非奇异","一阶顺序主子式为零","\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fa1178d771aa85be697585c83d2929e38.png\">对于矩阵 ,( )一定成立",{"answer":82,"createTime":5,"id":83,"options":84,"question":85,"source":23,"type":24},[],84480191,[8,9],"求解无约束非线性优化的FR共轭梯度法的\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002Fff79bca7a7caca8ba0e83a2e96177975.png\">表达为\u003Cimg src=\"https:\u002F\u002Ftihai-oss-cloud.itihey.com\u002Fimg\u002F4fe19217fe5833562ae3288a14b4fdb4.png\">",{"answer":87,"createTime":5,"id":88,"options":89,"question":90,"source":23,"type":24},[],84480197,[8,9],"若系数矩阵A严格对角占优,则J迭代法、G-S迭代法和SOR法均收敛",{"answer":92,"createTime":5,"id":6,"options":93,"question":16,"source":23,"type":24},[],[8,9]]