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对于 3 次样条函数 [tex=1.857x1.357]gYreUQsCp15jNr3_9D7PZA[/tex],如果给定的条件是[tex=10.857x1.429]liJOnccKszYEOatpmIE3w0-adYvyLfu7jrGgTbJUogiP9LY1f7ztCWBiuF6n5Dc2NOWfU_3Q6yZR9JgOoT5udRA8gq15Uu6Xb1549CXYi4Y[/tex], 如何给出边界条件使得[tex=1.857x1.357]gYreUQsCp15jNr3_9D7PZA[/tex]唯一确定。

对于 3 次样条函数 [tex=1.857x1.357]gYreUQsCp15jNr3_9D7PZA[/tex],如果给定的条件是[tex=10.857x1.429]liJOnccKszYEOatpmIE3w0-adYvyLfu7jrGgTbJUogiP9LY1f7ztCWBiuF6n5Dc2NOWfU_3Q6yZR9JgOoT5udRA8gq15Uu6Xb1549CXYi4Y[/tex], 如何给出边界条件使得[tex=1.857x1.357]gYreUQsCp15jNr3_9D7PZA[/tex]唯一确定。

发布时间:2025-06-23 04:58:05
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答案:解: 由于gYreUQsCp15jNr3_9D7PZA在jjHo0FhXIXsJ6R8tOMWUocRmVKfQDLlmAqcU8zom4Zs上是 3 次多项式, 故YE8Uet0b0wL46rfonUwN0yDqOpmXctIGICWIDpclyGQ在jjHo0FhXIXsJ6R8tOMWUocRmVKfQDLlmAqcU8zom4Zs 上是 1 次多项式. 而且满足YE8Uet0b0wL46rfonUwN0-Eq96x5wGpmu_yHj8_zq_dpD4n22NTw_Mt4gG8Jc8micGaDp03kGmgDC4xYQIzAygeWCB0Rw3U95-OT1Yg9RIbmIvfGFQnOAVZrgm8uMHgjHA0VfiyMbuvFJeZ0qy4o0--BSDMgp0N8bT3PCdRL-_r2AB3jM8_qJegB-8AsIW2B, 因此可表示为 YE8Uet0b0wL46rfonUwN0ytc_TZfhZOx7ZCKxWY2xyoqXjCOhpimkG-wO_tO89uKkHJkbOFEqQm130g5V7_ywwhUgD5RfiitIgvJhQYysE_U6TcXt0ylbgeF0of02MoX 于是积分两次并利用 fBvqIIyYmBZg_i5vd8DEfFTks8BtsYNLAhYqY9GYd-qjVbD6wBXNOjJ5knMuc0XhSSKuhQb4c6ktvyFpnhiWw_CANFkfnmqb_GanUt6xPGI 为未知量) 可定出积分常数: yV-pBxu61qGyw2z4R2FzMQ693iAOIToE8g1z8NH1nL_dJfKtgsMrwWMr-SSOHS-mcwSoPUApm-qhijoh78LeMJRhHx9i_KL-G0zIc_aqbq57SuKr4lO7o5DQxI0E_OD9ES4q0dwU-3700H_XRsWVtvnk_JfW__BK73OKnAkmTnBNIwlmZDvDTxxLsFFEkqhwLfBwKj5WbuN_YRi3y6wMvSoOC0KdFKmDmS8JTIYRK9hT7Vl30K-HWHa2p9Dimi4pbSIdwo24HAnghggVFrBRg56fH3SvOhD0tL99J0QUKObQhYBOHqrcRKH6AcZKYLF_cBqtaW-UPpR02vkqnhAXKA 事头上,积分两次后,记 yV-pBxu61qGyw2z4R2FzMQ693iAOIToE8g1z8NH1nL_dJfKtgsMrwWMr-SSOHS-mcwSoPUApm-qhijoh78LeMJRhHx9i_KL-G0zIc_aqbq57SuKr4lO7o5DQxI0E_OD9Gxb7S1TE3iwTEA4qkrYA9ZP2AhXGcqaO5NROZ5eg6lwVNhoUvcrIk_sQ42I4werPIREPVOjd6OtCTEY_mklHKfqq-PZ4L8UvcId5Kqa-BjU 再由 fBvqIIyYmBZg_i5vd8DEfFTks8BtsYNLAhYqY9GYd-qjVbD6wBXNOjJ5knMuc0XhxkGMCSKUWsOHY_5asC6gjw可定出BJBNrUK9SIjIhb-_BKUqyJZJrk6qbynVOAnfrdD6N8c。于是: y_fO3x7Y1gtxCQjFzPw6cW1muykMMMCcS5kZk_DXNlTCA98SybWx8xuqn_sdveCTzFOffi5752VSrzZHgAXlGOkvdkXpeFhs0CANbEqbUAI_9uw3TUAKiSSR2_7yKe8B3srwaU4zaMdt8I4IbB4t2Kn8s4vLT6RX_LK1QvhJa2kKTdvXy5tgfajRN8RH9anxZpa6zHcVbCOAnqcFFVpYUNnV_bF8BXrAXnxH6jVlvkpFXLq1-ZCYr54VDyXJ955eN63TvpfIMQleMfXn1uKgAw 即 QBgxDcyoOj8wUVMaisc2V0lb20UOnxv50uamdrgOnA48ny7cAnATwIpZ8rEIlAhZJpcEhM9XaNrcqWQ7YjICpQ3iixEr4zVE5tbUKe7cxhaWEhGBhSZqDMR-l6FqgeD1rIwKIZizPklovzTa_kzXO8gEyotIHP0yfqx9JdBQWkM  8RZ7_0G65Btnm65mpgAWlqJFRQoErMzCRDWeOJkOES-i4iArO4xXL7MCS9EE1-LjQUrjz49lT9IgUx5gN7aFWN4ZmUWc6cID2RrWueO0L3xQ5mISrDVv8F-yKUjbUvWoPymI77Sn7kJXXFcFmgk0vl9IyyytmuPrywsvRutaLy0 若考虑在Ig7oziIsVS5oxGVOKDeYL4xWogUOuHH-E5rVJfAy5Es上, QBgxDcyoOj8wUVMaisc2V_tAVVQMSLiZfuy1Jhd4DC8ka8T1exM_IZz58Wwv5JhoESX2wZejWWNN4ddM_2YtuAcaivN_m-_laJvpWJYEFGPRTpkfXGHIEKYzkXVmW8hOFesHK9HZ5kwTQu5yiTrqDFCBku8D2IQn_T6IXPjW1f_6K2_wP4UpAr7YcJMmDdEi, 两边的 QBgxDcyoOj8wUVMaisc2V4U1u4Y4Lnyor82E_A4Va8M应相等,即: DR8kHmZzCGXTh4k3XKExB1WkmtIFffD61mliACwYt-R8BysKTGYaXLbBNZgQHt6dE3eflu2T9LBrScv_3sxL9VEGEHuzUsHGOQjmSkabhIpqPFg9re_ilOFhtC1qWPEvP9eGERYX54Lb0OtYpGPzgFb9p-sGrJzHJFE8lsmPybrE_yDi05g-wUSOMTakgLVb-9sp0RKayV-oIeWUyFLr_pzxsSE69qqz3cPMcWi60OwzRz44P8i94DXwhOlz3SH3vJtzCWNCHRXQmc1Et3nItQ 整理并记 2zpdk8OoKqQKJ_h6xft-F2PpmqbmqIEFVj7FDamMLD5NvIaJSS__kvwx7ESuh4JW4AtfC2vHuKmJ8UrMtLyr83ZJA1w3RhKAgK6Tr-Xnc-OArRJpVc81RhcvksRMzRsuSe3bQE1Ox_agnEsmv0nbHA, 得 DAeNFb4N1-rcviSaie8ONfhRoMlPIOW4BKsPWJ84ajD8mXaUHQZjR8vXEY-WaRdgjZlG4Z1AFoJC7aO7q3US7Ei1KplUlZtNK7CvEAIUW_si_bJkMkuNdDRfMc304ep2VndBf5_MjB9zbv2SCY05zNgqoOLkQoC5VmEITrgXzfeArSaCiW5AwfaDn8et257sDvFMpL-RV7XCwxT8rZPQgEvW6Wu5gUZH0G8usFV--Ig_GTVDBtpgKOzFqOEkHEtb 若给定边界条件5WNYRsYSNftI9fWwc-yC23FXy-Tn_UnO6ia3JWjtePbm2tIxQGKY0DS7tpKofW0OMbqnma1_E2Jawa1VP7UuNA, 则形成方程组: 7EJHVCtO2IWq3KpdB-jQskXl0zfnvLIVVwzuMWHlr0n-_h5BOSjEOTcXt9Jxwy3qmBKhmgEfn7qZDZRvmATlkpb-wNG3xxRHl2EDiLSkQAzUesR125h_s_AcECjdYcmABQ79zL0LIsn1lNmPMWy6JjQKvniehdIHMRQRKCxZ49NiwMS2x8Rvypy59phT4hWkRO0NfQE1UwR_ia4tFzlqKgFjmH-aRBxPotpdlNAJ63YHJmd6CzCMIRS_W3KukcPxjoukiP7JaCZFMiwR4DDZ0kgumzjjPBrUwmT30ksUQtMkKSLJLONdEifm_-EejffRZgaX8QmmDqGmBXfLyp6RmwMbAcjvNGLuv1fHzXNueGWNgFn8Iz-51WiyMtDzJSNfemjXbSWlWMac7z6sqlIYdqHykI0Z87dgTrAQ_bJmECjEOdHtHM0dKcNaxosoOI9g4mR8kWRnJONVu4d2xb0F1rVLZ3epv7Dx0dnbuApnziQY8frz_ssouX6oiu_a55O86KhnCxymJmKmFFAiDT4QY5y-lIT7xETJc07GYd74EmZaG6qiF8uYNy7rrfGcODE3fk07xyTtPrxlI-MkWqWzbiNpaeYgpsWI411DDEeWE45aBpd95HpCVD-FLdd11_HDmuYalhfifUvMSIUIhcI0_wnyoGcVM5BeuhWzWAFTpZkBcOKDyK3lvrnRSK3V44XtAzYUOp4wN8k5r34g247ELbLiuUJa2Ex5SrmNdepAt3CMlWxBkoI6s5gQbucOLvh_ 该方程组的系数矩阵为严格对角占优矩阵,故9lgUBjQ4uQkDNrIFxPmAxAwei一确定
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