畢業(yè)論文-hermite插值的若干問題研究-文庫吧資料
2025-01-24 07:41本頁面
【正文】 ain confirms that valuable and rare works of high quality always earn the longlasting high price. Chinese painting and calligraphy is still the pillar of the market. However, the overall sales rate has dropped slightly, which reflects the demand for the ordinary auction goods has weakened,” said the president of China Guardian’s Hu Yanyan. Besides, the entry of new buyers also makes certain changes to the direction of purchasing. In a word, the overall market trend is very unpredictable. Although China Guardian 2015 Spring Auctions has achieved remarkable results, it does not mean that the market has walked out of the predicament. We still have to wait for the big economic boom to invigorate the art market.” Even so, the hot pursuit of some special items appeared this spring. A special session of China Guardian Spring Auctions titled “Fine Gilt—Bronze Buddhist Images” achieved a great deal with total sales volume of million yuan and 92 percent sale rate. The 5th Shamar Rinpoche Statue from 1617th century of Tibet was sold for million yuan. The Beijing Chengxuan Auctions featured almost 2,800 items of coins and stamps in three sessions with good sale rate. The Huachen Auctions also set a special session of photographs under the condition of largescale decline of auction sessions. There was a palpable dull thud of disappointment that acpanied the return of the imperial entourage of Zhen Huan to her homeland. It followed a couple years of hushed excitement as Chinese fans were fed tidbits about their proud concubine who was supposed to conquer the high ground of the North American market. Zhen Huan is, of course, the title character of The Legend of Zhen Huan, a 2011 television series that swept China off its feet and later took other Asian countries by storm. Two years ago, it was reported that HBO, a premium cable service headquartered in the United States, was going to air it in North America after some modification. Now, a condensed version that provides English subtitles but no dubbing has finally been made available on Netflix for online streaming. This version, highly anticipated as a milestone in China39。s Poly Theater. Their show, titled Ulan Muqir on the Grassland, depicted the history and development of the art troupe. Being from the region allowed me to embrace the culture of Inner Mongolia and being a member of the troupe showed me where I belonged, Nasun, the art troupe39。s performers of the troupe still tour the region39。t have a formal stage. The audience just sat on the grass. Usually, the performances became a big party with local people joining in. For him, the rewarding part about touring isn39。80s. We sat on the back of pickup trucks for hours. The sky was blue, and we couldn39。s Shaanxi province pass through a stop on the ancient Silk Road, Gansu39。最后簡單討論了Hermite插值的優(yōu)缺點(diǎn)。通過兩個典型的Hermite插值的例子，說明建立Hermite插值多項(xiàng)式的方法。我知道，這篇論文還存在缺點(diǎn)和不足之處，但是它是一個起點(diǎn)，在此基礎(chǔ)上，我會更加努力，在以后的研究生學(xué)習(xí)中，不斷提高自己。謹(jǐn)向我的父母和家人表示誠摯的謝意，使他們不變的支持、無微不至的關(guān)懷，促使了我的前進(jìn)。各位老師對我的教育和影響，將使我終身受益。畢業(yè)設(shè)計(jì)和畢業(yè)論文寫作的經(jīng)歷和收獲，值得一生回味。這些都使我受益匪淺，并終身難忘。在大學(xué)期間陳老師教授過我《數(shù)值逼近》和《微分方程數(shù)值解法》兩門課程，共四個學(xué)期。Hermite插值具有少節(jié)點(diǎn)得到高次插值多項(xiàng)式的特點(diǎn)Hermite插值插值多項(xiàng)式靈活多樣Hermite插值在節(jié)點(diǎn)一定的條件下，可以多種構(gòu)造插值條件3 重節(jié)點(diǎn)插商與Hermite插值4 例題及解答例題 1 （兩點(diǎn)三次插值多項(xiàng)式） 已知在節(jié)點(diǎn)1,2處的函數(shù)值為 ，在節(jié)點(diǎn)1,2處的導(dǎo)數(shù)值為求的兩點(diǎn)三次插值多項(xiàng)式，及在處的函數(shù)值解： 作為多項(xiàng)式插值,三次已是較高的次數(shù)，次數(shù)再高就有可能發(fā)生Runge現(xiàn)象,因此，對有n+1節(jié)點(diǎn)的插值問題，我們可以使用分段兩點(diǎn)三次Hermite插值例2 （誤差估計(jì)）已知及其一階導(dǎo)數(shù)的數(shù)據(jù)見下表,用埃爾米特插值公式計(jì)算的近似值,并估計(jì)其截?cái)嗾`差.解： x121144 f(x)1112 f 39。Hermite插值的逼近函數(shù)與被逼近函數(shù)不僅在插值節(jié)點(diǎn)上取相同的函數(shù)值，而且逼近函數(shù)與被逼近函數(shù)在插值節(jié)點(diǎn)上去相同的若干階導(dǎo)數(shù)值。滿足，就稱為關(guān)于節(jié)點(diǎn)的二重Hermite插值多項(xiàng)式。證畢定理 3（Hermite插值余項(xiàng)定理）Hermite插值公式的余項(xiàng)為其中， 是插值區(qū)間內(nèi)的某一點(diǎn)證明：引進(jìn)輔助函數(shù)由條件（1）知 即有個單根和r+1個二重根由Rolle定理知，在內(nèi)至少有n+r+2個零點(diǎn)，至少有n+r+1個零點(diǎn)依此類推可知：在內(nèi)至少有一個零點(diǎn)因此即得 若，則響應(yīng)的Hermite差值多項(xiàng)式為 (11)其中余項(xiàng)公式為：特別當(dāng)時，插值條件為：由此得三次Hermite插值多項(xiàng)式：(12) 多項(xiàng)式（12）常用作分段低次插值，稱為分段三次Hermite插值2 兩點(diǎn)三次Hermite插值及其余項(xiàng) 兩點(diǎn)三次Hermite插值先考慮只有兩個節(jié)點(diǎn)的插值問題：設(shè)在節(jié)點(diǎn)處的函數(shù)值為，在節(jié)點(diǎn)處的一階導(dǎo)數(shù)值為，兩個節(jié)點(diǎn)最高可以用3次Hermite多項(xiàng)式，作為插值函數(shù)應(yīng)滿足插值條件：
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