Arnold's interest in Newman the man and the thinker is intense at every period of his life. There is no other relationship quite like it in Arnold's career: no other man of the nineteenth century — neither Goethe, nor Sainte-Beauve, nor Emerson, nor Carlyle, nor Wordsworth — evoiked from Arnold such a continuious and detailed intellectual response combined with such an intense personal veneration. [152-53]
Newman almost certainly provides Arnold with many of his basic notions and terms and which very likely inspired the deep-running dualism that a number of readers have detected in Arnold's ideal.  Despite his asserted ideal of human nature brought to perfection on all sides, Arnold was fundamentally too conservative ever to give up . . . the historic Christian dualism between nature and grace, morality and reason — the dualism that also provided the rock on which Newman's view of 'intellectual culture' also foundered. 78
Two of Newman's most characteristic teachings — on the existence of a privileged spiritual elite and on the sharp discrimination of moral and intellectual truth — . . . are two ideas that absorb a great deal of Arnold's attention during these crucial first years of the formation of his critical doctrine." 
Not surprisingly, Arnold and Newman also coincided in their contempt for radical, religiously and politically subsersive solutions to the problems of the century — for example Benthamism and Comteanism, which might be regarded as extreme extensions of Liberal principles. In 'The Tamworth Reading Room' Neman had spoken of Bentham, who had not a spark of poetry in him, at length and with entire scorn; and in The Idea of a University Bentham is seen, along with Hobbes and Hume, as 'simply a disgrace.' Arnold, too, spoke of Utilitarianism as being 'doomed to sterility. 
Arnold's strategy is complex. Against orthodox Christians he argues that the notion of a Personal God is unintelligible and unverifiable — according to a special notion of verification. Against the rationalizing philsophical Liberals (whose positivism he accepts) he argues, nevertheless, that the masses need emotional and imaginative support for the practice of morality, and this can come only from the Bible.  . . . Finally, against what Arnold sees as the compromising non-Christian but heistic devotees of Unitarianism, he argues that there logic is unsound, since they reject individual Christian doctrines as incredible or irrational but fail to recognize that Christian theology is a logically valid concatenation of probabilities and that only by striking at the very root of all theology can individual Christian tenets be cast down. 
Buckley, J. H. The Victorian Temper: A Study in Literary Culture. Cambridge: Harvard UP, 1964.
DeLaura, David J. Hebrew and Hellene in Victorian England: Newman, Arnold, and Pater. Austin: U of Texas P, 1969. [full text]